My 1 Year Diagnosis Anniversary (Yesterday)!

One year ago yesterday, on Friday, December 3, 2010, I received my diagnosis of appendiceal adenocarcinoma!  Thank God I'm still around one year and one day later!  With N.E.D. (No Evidence of Disease) as of my most recent CT scan, which I had in early September 2011!  Looking back over my one year and one day of knowing that my useless appendix had tried it's best to kill me off by developing an adenocarcinoma (without my permission!) that had escaped the bounds of my traitorous appendix and was metastasizing all over my peritoneum (also without my permission!), it has been quite a journey, indeed!

Needless to say, I know I wouldn't be here at all without the countless numbers of prayers and positive thoughts and best wishes that have been offered on my account for at least a year and a day!  Please keep it up, if it's not all that much trouble (or even if it is a little bit of trouble--it's well worth the effort), it's really been working wonderfully well!  Prayers and positive thoughts and best wishes are never wasted but are always recycled and reused and continue working their miraculous effects, if not always on the prayee, most certainly on the prayor!  There's only one Multiverse that we all happen to be inhabiting at this moment and we're all in it together!

The Nobel Laureate physicist Richard Feynman once hypothesized that the reason that all electrons everywhere where absolutely identical (so that it's theoretically and experimentally impossible to distinguish one electron from any other electron) was that they were all the very same electron doing an incredibly complicated dance going forward and backward in time (apparently you can go back in time to some extent if you are small enough that your true quantum mechanical nature manifests itself!--an electron going backwards in time appears to us in the macroworld as a positron, an anti-electron, going forwards in time!), a most provocative and seductive hypothesis, indeed!  Extrapolating to all the (apparently) different types of "fundamental" particles, all red up quarks are identical because they are all the very same red up quark also dancing forward and backward in time all over the known (and unknown) Universe, all muons are identical because they are all the very same muon dancing forward and backward in time all over the place, yada, yada, yada!  And, extrapolating just one little theoretical baby step further, since all the (apparently) different types of "fundamental" particles are almost certainly (at least in our theoretical physics dreams!) just various aspects of one underlying super-great-great-great-grand unified Ur-particle (usgggguUp), we're all made up of the one usgggguUp and therefore all intimately connected (entangled!) at the deepest of levels!  Remember that the next time "you" treat "others" in the very same way that "you" would like to be treated!

Still Very Much Alive and Kicking and Glad to be so!

I realize that I haven't posted much lately!  I've been luxuriating in my continued NEDness (No Evidence of Disease)!  I take the lack of evidence of disease to be indicative of being "cancer-free," fully aware that this could all change with the next CT scan, which is scheduled for Wednesday, January 11, 2012.  All CT scans, even the high-resolution ones at MDACC (M.D. Anderson Cancer Center) here in Houston, Texas, necessarily are limited at some level in the resolution they can achieve, whether it's 1 mm or 0.5 mm or whatever--current CT scan imaging technology isn't able to resolve individual cancer cells at the 10 micron level or so, and since the energy of the photons used goes up as the corresponding wavelength goes down (cells and other structures much smaller than the photon's wavelength can't scatter the corresponding photons all that well!), you probably don't want to be exposed to a lot of very short wavelength x-rays (or gamma rays) in order to achieve that kind of resolution!  Perhaps thermal neutrons could be used, however!  They might not damage your tissues nearly as much as the high-energy x-rays (or gamma rays) do!  Nevertheless, psychologically, it's much easier to deal with the idea that I'm completely "cancer-free," even though my oncologist would never tell me such a thing!  To paraphrase that great patriot, Patrick Henry, "Give me cancer liberty or give me death!"

Cancer death is, of course, weighing on everybody's minds, mainly as a result of the passing of Steve Jobs!  The parts of his 2005 graduation address at Stanford that I've seen are very prescient and wise!  Life is, indeed, far too short for any of us to waste much of it living someone else's life, trying in vain to meet someone else's expectations for our lives.  Death can be a gift that makes each and every moment of each and every one of our lives all the more precious and unique!  There are, after all, only 86,400 seconds in each 24 hour day of our lives, so be careful not to squander too many of them in worthless pursuits that don't engage all of your passions!  Do what you love (whatever that is) and love what you do (whatever that may be)!  Love wastefully and recklessly because there's no way in heaven or on Earth that we can ever exhaust the true fount of love!  Not only can love be unconditional, love can be inexhaustible and infinite beyond all imagination and reason!  Thanks, Steve!  I love my iPad, my iPods, and I'm sure I'd love an iPhone, too, if I had one!  Thanks also to Dave and Jo and Brian and Celeste, of course, without whom we'd never have had the pleasure of getting to know and use Paddy the iPad!

Thank God for N.E.D.!!!

We're quite pleased to be able to report that the results of my most recent CT scan show N.E.D. (No Evidence of Disease)!  And all the cancer/tumor markers in my blood are at normal (not elevated) levels!  Praise God!  Prayer works miracles!  I'm good for at least another 3 months or so (until my next CT scan)!  I love N.E.D.!  Better N.E.D. than dead!  We're elated, of course!  I'll find out tomorrow whether I need another chemo treatment or not (I'm hoping not, but if I do need to get one more chemo treatment--icing on the cake, making the rubble bounce [to mix metaphors!], then so be it!)--Thanks again for all your positive thoughts and vibes and prayers and best wishes!  They're all appreciated so much, as are you all!  It's such a wonderful, blessed relief to be free of cancer anxiety for a while!  Doxa soi, Kurie!  {Hellenistic Greek meaning "Glory to You, Lord!"}

On pins and needles (figuratively, of course!)!

Caroline and I go in to M.D. Anderson Cancer Center (MDACC) this afternoon to meet with my wonderful, wizardly surgeon, Dr. Paul Mansfield!  We'll learn the results of my most recent CT scan (Computerized Tomography, an amazing way to get exposed to the equivalent of hundreds, if not thousands, of chest x-rays all within the space of half an hour, at the most!), which I had over a week ago, on Wednesday, September 7, 2011 (which also happened to be the 60th wedding anniversary of my Uncle Dick and Aunt Helen, and which also was one day before the 55th wedding anniversary of my parents, Burr and Cynthia!)--it has been a little nerve-wracking waiting to get the results of the CT scan.  We're sincerely hoping and praying that the result is N.E.D. (No Evidence of Disease)!  If we do get the result of N.E.D., that would be truly wonderful!  I may not even have to take another chemotherapy treatment, which I'm currently scheduled to receive tomorrow!  On the other hand, if there is still some E.D. (Evidence of Disease, not Environmental Defense or that other "ED" that involves little blue pills!), that will, of course, be somewhat disappointing, but at least we will know more about what's going on with any tumors that happen to be hanging around, uninvited and definitely unwelcome, in my body!  We're scheduled to meet with my wonderful, sagacious colorectal oncologist, Dr. Imad Shureiqi, tomorrow to further discuss the CT scan results (whatever they are!) and determine where we go from here, treatment-wise!  As is said sometimes in Latin, Dum Spiro, Spero (while there's breath, there's hope!)!

Mid-Life Metanoia: Run! Middle-aged woman trying to learn to blog!

I highly recommend Sharron Cox's new blog about her experiences attending the Episcopal Seminary at Sewanee in Tennessee--Enjoy!

Mid-Life Metanoia: Run! Middle-aged woman trying to learn to blog!: From a simple e-mail with instructions and encouragement from friend Christi, I am attempting to start a blog on my excellent, ecclesiastica...

An Obvious Mathematical Breakthrough!

Bill Gates, in his fascinating book The Road Ahead, first published in 1995 (the same year I graduated from the Georgetown University Law Center!), presciently foresaw what he called "an obvious mathematical breakthrough," namely, "development of an easy way to factor large prime numbers."  I'm happy to announce that I've managed to make this obvious mathematical breakthrough!  Give me any prime number, no matter how large, and I can develop an easy way to factor such a large prime number!  For example, you can give me the 225 digit prime number: 

3011684434270246290531649722016778440996627108537 4051680825787892441039027182441095592352415876075 3504018345029958824712015457312062590110182837940 9572517144993258842135900335759766170969093183692 46861620075335839843749999903 ,

and I will factor it as follows: since this 225 digit prime number is a prime number, it must necessarily have 2 and only 2 factors, 1 and the 225 digit prime number itself!  Of course, I'm not the first person to solve this somewhat trivial problem posed by Bill Gates (undoubtedly inadvertently and/or accidentally--he's obviously been the victim of a poor proofreader!)--for example, Wolfram's wonderful website notes this statement in the last paragraph of the entry on prime numbers!  By the way, my chemo treatments are going miraculously well, thank God!  Keep all those prayers and good wishes coming my way--they really are helping a lot!  10 chemo treatments down and only 2 left to go!  Here's hoping that my next CT scan (scheduled for early September, shortly after our 14th anniversary on August 30th) will show no trace whatsoever of any cancer or tumors, because they will all have been annihilated and thoroughly terminated with extreme prejudice!  Amen!                                                                                                                                                                     
                                                                                                                                                              
                                                                                                                                                              

Nine Down, Three to Go!

I'm very pleased to report that I've successfully received 9 rounds of chemotherapy treatment and only have 3 more chemo treatments to go to complete a total of 12 rounds of chemo!  I'm even more pleased to report that I haven't suffered any side effects from the FOLFIRI chemo treatments!  Praise God!  All the myriad prayers being offered up for me must be storming the gates of heaven, indeed!  I am so very blessed and I joyfully thank God every day for the wonderful daily bread of my existence!  There's nothing like a potentially life-threatening illness to focus your mind on what truly matters the most!

I go to MD Anderson Cancer Center here in Houston, Texas, every other week to receive my chemo treatments.  According to my current schedule, if everything goes as planned, I should be finishing up my 12th round of chemo treatments by mid-September 2011!  My next CT scan is scheduled right after Caroline's and my 14th wedding anniversary on August 30, 2011!  Hopefully that CT scan will show what my most recent CT scan, taken after I'd recovered sufficiently from my 12 hour HIPEC operation, showed, namely, nothing at all, and, in particular, no signs whatsoever of any tumors anywhere!  Approximately one-third of all patients who undergo the HIPEC surgical procedure have a complete and total remission of their peritoneal cancers (at least for 5 years or so) and I naturally assume I'm in that group of the one-third of all patients!

I am also very pleased and proud to report that I was recently offered (and accepted, of course) the position of in-house Patent Counsel/Physicist with Muons, Inc., a scientific research and development company dedicated to "innovation in research" that specializes in coming up with improvements for particle accelerators used in a plethora of industrial and medical and fundamental scientific research applications.  One example of the wide range of research interests of Muons, Inc. is the development of accelerator-driven sub-critical nuclear waste transmuters that are fully capable of generating significant amounts of safer, cleaner, and greener thermal and electrical nuclear power while transmuting large quantities of harmful and dangerous high-level radioactive nuclear wastes from conventional nuclear power plants into much smaller quantities of much less harmful and much less dangerous low-level nuclear radioactive nuclear wastes!  I'm very excited by the challenges and opportunities afforded by working with Muons, Inc. and optimizing their intellectual property protections and burgeoning patent portfolio!  It's a great position, amazingly well tailored to my background in both physics and patent law!

By the way, in case you were wondering, muons are fundamental subatomic particles that are identical to electrons in every respect, except that they are about 207 times more massive than electrons and decay into electrons and neutrinos (both electron-type and muon-type) with a half-life of about 2.2 microseconds!  Another focus of the research interests of Muons, Inc. is the development of viable muon colliders!

Back on Chemo Sabe!

Sorry for the overly long "radio silence"!  I didn't mean to neglect my blog posting duties, but somehow I never got around to posting anything on my blog since the day after my surgery!  So much has happened since then!  Where to begin?  Well, I've recovered sufficiently from my 12 hour HIPEC surgery to be back on chemotherapy!  Even as I'm writing this blog post, 5.2 ml/hour of 5 Fluorouracil is being pumped directly into my jugular vein through my Bard Power Port-o-Catheter by a little battery-powered pump in its own little fanny pack, my constant and somewhat annoying companion for 46 hours from when I left M.D. Anderson Cancer Center (MDACC) yesterday around 1:30PM until I return there to be disconnected tomorrow morning around 11:30AM, right after church at Grace Episcopal Church!  Because my colorectal oncologist, the amazing Dr. Shureiqi, feared that the peripheral neuralgia side effects from the Oxaliplatin that I'd been getting in my 5 previous chemo treatments with FOLFOX, and that I also got during the HIPEC perfusion during my 12 hour surgery, might become a permanent chronic condition, I'm now on a slightly different chemo cocktail, FOLFIRI, which is an alternative chemo treatment that has similar effects on colorectal cancers that FOLFOX has, substituting Irinotecan, a topoisomerase inhibitor that prevents DNA from uncoiling from the histones it's wrapped around thereby inhibiting rapid cell growth typically found in tumor cells, for Oxaliplatin.  The side effects of FOLFIRI can be somewhat different than the side effects of FOLFOX.  For example, unlike FOLFOX, FOLFIRI does not cause peripheral neuralgia in one's extremities such as numbness and tingling in one's fingers and toes and feet and hands.  FOLFIRI also, thankfully, does not cause the weird and uncomfortable feeling in one's throat when one consumes one's favorite iced quad espresso beverage from Starbucks!  In some cases, FOLFIRI has been known to cause loss of head hair and bouts with diarrhea, which is why I've stockpiled lots of Imodium!  So far, knock on wood, I've been spared these side effects, but it may be way too early for any of these side effects to have shown up!

My hospital stay at MDACC was not bad at all and was blissfully and miraculously short and sweet--I was discharged one day shy of 2 weeks after my surgery on April 12, 2011, on Monday, April 25, 2011.  The only minor complication I had was a couple of places along my cubit-long incision (stretching from my breast bone to my pubic bone, skirting around my innie belly button!) that had somehow become infected.  The infection was quickly tamed with IV antibiotics administered while I was still an in-patient at MDACC.  I did have to leave MDACC tethered to a portable Wound Vac, which continually sucked out discharges and debris from the two fairly sizable wounds, both over 2 inches (5.08 cm) deep, that were dressed in a special type of dressing that had to be changed every 2 or 3 days by a home healthcare nurse, in my case a wonderful woman named Abby!  When I was first discharged from MDACC, Caroline and I stayed at my parent's home in Meyerland.  Caroline was working during the day, so Burr and Cynthia very kindly nursed me back to health with copious heaping helpings of tender loving care!  Much to my delight (and recovery) I discovered that you can go home again!  Even if only for a short while!  At first, because of my incision and its healing wounds, it was a bit uncomfortable for me to lie flat on my back in bed at night--the hospital bed was always inclined at a slight angle!  Fortunately, I discovered that the reclining chairs in my parent's living room were quite comfortable and I was able to sleep many a happy hour there in the chair!  In addition to pampering and spoiling me, Burr and Cynthia were also very good about encouraging me to get up every now and then during the day and go for a walk in the neighborhood, at first just up and down Darnell, but eventually extending all the way around the block along Carew back to Darnell!

All in all, my recovery has been nothing short of miraculous!  I attribute all the healing to the plethora of prayers and positive thought energies being offered on my behalf and being sent my way!  Thank God our God is a consummate God of healing, wholeness, and wellness!  I have truly been blessed in countless ways!

I was especially blessed by all the wonderful cards and flowers and balloons and plants and, most of all, in person visits while I was in the hospital at MDACC--you have no idea how welcome you all were and how happy you all made me (and you all know who you are!)--it really makes a world of difference!  The doctors and nurses and all the staff and the volunteer corps at MDACC couldn't have been more attentive and more helpful than they were--I almost didn't want to leave!  They had me up and walking the very next day after the 12 hour surgery, amazingly enough!  In seemingly no time at all I had graduated from a pure "liquid" diet, to the "soft food" diet, and on to the full "regular" diet!  My internal plumbing apparently was hooked back up in expert fashion, so even though I was missing the whole right half of my large intestine (yes, I now have a semicolon!), small bits of my small intestines, my traitorous appendix, about 32 or so lymph nodes that had been draining the cecum I no longer had (about 8 of which lymph nodes showed some involvement with the tumors, according to the pathology report, which is a very good reason for me to continue with 12 full rounds of chemotherapy!), and 40 to 50 small metastatic tumors that were surgically removed from my abdominal cavity before the HIPEC perfusion, along with my gall bladder, which was removed not because of any tumor involvement necessarily, but because it didn't look very "happy"(!), all the remaining pieces of my digestive system were functioning excellently in no time at all!  By the way, you never appreciate how much you rely on your abdominal muscles to do pretty much anything like standing up, sitting down, walking, and even ooching yourself over a bit while in bed until you can't use your abdominal muscles any more because they've been cut through so the surgical team can access your innards!  Evidently, in my case, for mysterious reasons, there were a couple of extra inches of adipose tissue that also had to be cut through in order to successfully complete the surgery!  Go figure!  I had asked whether the surgical team could do a little liposuction while they were in there anyway, but apparently that's not one of the surgical options available at MDACC at this time!

We met with my miracle-worker surgeon, Dr. Paul Mansfield, on Thursday, May 12, 2011, 4 weeks and 2 days after the grueling 12 hour surgery on Tuesday, April 12, 2011.  He thought the incision wounds had healed enough that I didn't need to be tethered to the Wound Vac any more and he also, thankfully, decided that I no longer needed the "G-tube" to my stomach that I'd had ever since the surgery in case I ever got nauseated and needed to empty my stomach contents other than by the usual route, which fortunately I never did!  The G-tube, even though it was never used, still had to be flushed with 30 cc's of tap water and redressed every day, not to mention the fact that the proper stopper for the G-tube had somehow gotten misplaced while I was still in the hospital at MDACC so that there were a couple of accidental and messy leakages from the G-tube before I figured out a foolproof way to tape the substitute G-tube stopper so that it couldn't just blithely pop out!  Dr. Mansfield was able to extract the G-tube right there in the examination room in the Gastrointestinal Clinic before I even knew that he'd done it--truly a wizard, indeed!

You'll be pleased to know that I've continued my assiduous studies into the wonderful and sublimely mysterious world of number theory, having worked my way through all the exercises in Robert Daniel (R.D.) Carmichael's masterful (and free, thanks to Project Gutenberg!)1914 (safely in the public domain!) classic entitled The Theory of Numbers, which I'd downloaded as a PDF file onto Paddy the wondrous iPad!  You'll also be pleased to know that I have nothing further to report regarding Furlong's Conjecture (see previous postings, one by that name and another that's incredibly long and virtually impenetrable!), which, as some of you all may remember, narrows Brocard's Conjecture significantly (Brocard conjectured that there were at least 4 prime numbers between successive squares of odd prime numbers--a prime number being, of course, any number greater than 1 that has 2 and only 2 divisors, namely 1 and itself, whereas I conjectured that there were at least 2 pairs of "twin primes" between successive squares of odd prime numbers, where "twin primes" are prime numbers separated by one and only one composite, non-prime number--if my conjecture is ever proven to be true, then Brocard's Conjecture follows as a necessary corollary, since 2 pairs of "twin primes" necessarily includes 4 prime numbers!) in that Brocard only requires 4 prime numbers that could each be separated from each other by some number of composite numbers while I specifically require my 4 prime numbers to be arrayed into 2 pairs of "twin primes"!  I have yet another conjecture involving "twin primes" that narrows Legendre's Conjecture, but it's a little more complicated to state.  Legendre conjectured that there will always be at least one prime number between successive square numbers (for example, between 1^2=1 and 2^2=4 there are the prime numbers 2 and 3, and between 2^2=4 and 3^2=9 there are the prime numbers 5 and 7, etc., etc.), but I go on to conjecture that there is at least 1 pair of "twin primes" between successive square numbers greater than 1, or, if not, then there will always be at least 2 pairs of "twin primes" between neighboring successive square numbers!  For example, you can easily verify that my conjecture holds true between 2^2=4 and 3^2=9 (the pair of "twin primes" being 5 and 7), between 3^2=9 and 4^2=16 (the "twin primes" 11 and 13), between 4^2=16 and 5^2=25 (the "twin primes" 17 and 19), between 5^2=25 and 6^2=36 (the "twin primes" 29 and 31), between 6^2=36 and 7^2=49 (the "twin primes" 41 and 43), between 7^2=49 and 8^2=64 (the "twin primes" 59 and 61), and between 8^2=64 and 9^2=81 (the "twin primes" 71 and 73).  Note, however, that there are no "twin primes" between 9^2=81 and 10^2=100 (the only primes between 81 and 100 are 83, 89, and 97, none of which are "twin primes").  Therefore, since there is also no "extra" pair of "twin primes" between the neighboring square numbers 8^2=64 and 9^2=81 (the one and only pair of "twin primes" between 64 and 81 are 71 and 73!), in order for my other, more complicated conjecture to hold true, there better be at least 2 pairs of "twin primes" between the other neighboring square numbers 10^2=100 and 11^2=121 (and, sure enough there are, the "twin primes" 101 and 103 and 107 and 109!)--I've checked successive squares up through 31^2=961 and 32^2=1024 and as far as I can tell, my other, more complicated conjecture holds true at least up to 1024, which is a lot smaller than countable infinity, but at least it's a very small and modest step in the right direction!

I survived my 12 hour surgery and am doing well, indeed!

Twelve long hours seemed like no time at all, at least to me! I'm sure 12 long hours seemed like 24 longer hours to Caroline and Burr and Cynthia who maintained a vigil for me in the waiting room here at M.D. Anderson Cancer Center! As long as I can keep giving myself shots of pain killer through my epidural every 10 minutes or so I'll be fine! Already, I've sat up in a chair twice and walked thrice around the nurses' station! I've already been blessed by many wonderful visitors, most especially Caroline and Burr and Cynthia! Dad's very kindly volunteered to spend the night with me, folding himself into the chair/cot in the room! Prayer continues to lift us all up, especially me! Praise God for the good outcome!

D-Day is Here and H-Hour is Almost Upon Us!

Less than an hour from now the alarm clock in my cell phone will go off, indicating that it is 4:00AM Central Daylight Time here in Houston, Texas. It will be time for me to wake up (assuming I ever get to sleep!) so that we can report to M.D. Anderson Cancer Center for my long-awaited surgery for the metastatic appendiceal adenocarcinoma, the appendix cancer that has enjoyed the hospitality of my abdominal cavity far too long! Tumor or not tumor, that is the question, to which my emphatic answer and that of my wonderful surgical team led by Dr. Paul Mansfield is a resounding "Tumor no more!!!" I know I should be sleeping right now, but I'll get hopefully 10 hours or more of blissful "sleep" while anesthetized during my surgery which is due to commence sometime around 7:15AM today!

Thank you all so very much for all your myriad thoughts and prayers for me and for my wonderful loving wife Caroline and for my wonderful loving family! I really do feel lifted up, so all your kind thoughts and best wishes and prayers of any kind have been quite effective. I'm as calm and relaxed as anyone could be under the circumstances! I have complete and total confidence in my whole team, especially in my team leader, Dr. Abba Father God Almighty, Maker of Heaven and Earth, Ground of All Being, Power Set of the Set of All Sets (for all you mathematically inclined disciples), divinely revealed to us by the profound and ineffable humanity of His Son, my Lord and Savior Jesus Christ, in Whom I live and move and have my being, Who is my true life, dwelling in me bodily with His Holy Spirit! This present illness is not unto death, but is for the greater glory of God! May God bless you all and guard you all, may He make His face shine upon you all and have compassion upon you all, and may He lift up His face upon you all and give you all peace!

Happy PI Day to One and All!

As I'm sure most of you all were aware, today, March 14th or 3/14 (as we say in the USA) is Pi Day! At 1:59:26 AM and PM, the date and time conspired to produce the first 8 digits of the decimal expansion of Pi, the ratio of the circumference of any circle to the diameter of that circle! I trust you all celebrated accordingly!

On the appendix cancer front, we (Caroline, Burr and Cynthia, and Brother Norman, and me) met with my surgical oncologist, Dr. Paul Mansfield, and he recommended surgery to remove all the tumors from my abdominal cavity. The surgery is tentatively set for Tuesday, April 12, 2011. Depending on how involved the lymph system is, Dr. Mansfield will make the call during the surgery about whether or not to use the Hyperthermal IntraPeritoneal Chemotherapy (HIPEC).

Great news! Thank you, Lord, for all your many blessings, most particularly for Caroline and the rest of my loving family.

In case you were wondering, especially on PI Day, here are some more decimal digits of PI:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 ...

Great News About My CT Scan!

I finally got my long-awaited CT scan last night around 8:00PM (it was originally scheduled for 6:00PM, but that's par for the course!--it's why we're called patients, I guess!) and, fortunately, the pros at MDACC were able to quickly analyze the CT scan results overnight so that when we met with my wonderful colorectal oncologist, Dr. Imad Shureiqi, today at 1:30PM he was able to give us (me, Caroline, Burr, and Cynthia) the good news--the tumors had not grown at all since the previous CT scan taken on December 13, 2010, there were no new metastatic nodules, and the tumors had not spread beyond the peritoneum!!! There were no "spots" on my liver or pancreas or kidneys or lungs or heart or anywhere outside my abdominal cavity! The primary appendiceal adenocarcinoma was about the same size as it was in December, maybe even slightly smaller (I can't recall the exact dimensions, but I don't think any of the lineal measures of the appendix tumor were more than 3 centimeters, a little over an inch, about 1.18 inches at 2.54 centimeters to an inch, so the primary tumor has never been more than 27 cubic centimeters in volume, or 1.64 cubic inches), and the 4 metastatic nodules on my peritoneum were all still each less than about 1 cubic centimeter in size, which is about 0.061 cubic inches. And there aren't any more nodules! No new nodules! The lymph nodes around the appendix are no larger than they had been before! The chemotherapy, FOLFOX6, has apparently succeeded in stopping the cancer in its tracks! Praise God! Hallelujah! Hosanna in the Highest! Thank you Lord!


The next step is to meet again with my surgical oncologist, Dr. Paul Mansfield, to discuss whether it makes sense to pursue surgical options, such as Hyperthermal Intraperitoneal Chemotherapy (HIPEC), at this time. Hopefully, Dr. Mansfield will want to do the surgery! It's not any easy surgery to endure. It can take up to 14 hours! That's a long time to be under general anesthesia! The HIPEC part of the surgery itself includes 90 minutes or so of my being gently rocked back and forth while the warm chemo bath is sloshing around inside my abdominal cavity! The direct application of the chemo to the affected tissues is much more effective than chemo delivered intravenously, which, because it's necessarily delivered systemically throughout the whole body cannot be nearly as concentrated or as strong, because of the deliterious consequences of the deadly chemo cocktail. Supposedly, one-third of the patients who under go the full HIPEC treatment experience a complete remission of their cancers with no reoccurence of the cancers! I intend to be in that one-third! Those are good odds, indeed! Much better than the odds of winning the lottery, for example!


Needless to say, we're all very pleased by all this! Ecstatic, you might say! Euphoric! I'm still at MDACC getting my fifth FOLFOX6 chemo treatment, fifth out of twelve altogether. Thanks to Dave and Jo and Brian and Celeste, I'm able to post this in real time using our beloved Paddy the iPad! We love Paddy and can't imagine what it would be like living without it!


On an entirely unrelated note, for all of you who are wondering about the fate and robustness of Furlong's Conjecture (see previous posting of the same name--basically, I modestly conjectured that there will always be at least two twin prime pairs between the squares of successive prime numbers!), here's the latest and greatest that I've been able to coax out of Excel (equipped with an add-on that permits virtually unlimited precision integer operations and many very handy number theory operations to be performed--for more, see Joe Crump's Immortal Theory Number Theory website), although not without a lot of tsuris (Yiddish for trouble) and much kutput (Gujarati for trouble):


My nifty Factorizer program (not programmed by me, of course, but able to be purchased for a modest sum at Factorizer) found 531 prime pairs in the range from 2,141,005,441=46,271^2 [2.141005411 billion or 2.141005411x10^9, a 10 digit number] through 2,141,190,529=46,273^2 [2.141190529 billion or 2.141190529x10^9, a 10 digit number]. Needless to say, my conjecture is certainly robust enough (with 529=23^2 prime pairs to spare!) out to 46,271^2 and 46,273^2!!! Unfortunately, Factorizer does not do numbers larger than the Mersenne prime M_31=2^31-1=2,147,483,647 so I was forced to turn to my makeshift Excel number theory kluge!


Between (2,141,190,431)^2=4,584,696,461,805,965,761 [4.584696461805965761 quintillion or 4.584696461805965761x10^18, a 19 digit number] and
(2,141,190,433)^2=4,584,696,470,370,727,489 [4.584696470370727489 quintillion or 4.584696470370727489x10^18, a 19 digit number] there are at least 1863 twin primes between (2,141,190,431)^2=4,584,696,461,805,965,761 and 4,584,696,461,808,572,881 (with 8,564,761,728 - 2,607,120 = 8,562,154,608 [8.562154608 billion or 8.562154608x10^9, a 10 digit number] numbers in the range to spare)!!! The range of numbers chosen is not completely arbirtary! It merely reflects the fact that Excel only permits 65,536=2^16 rows in any worksheet and I'm too lazy to start another column of prime numbers, so for each range of numbers I'm really only sampling the first 60,000 or so numbers in each range (for reasons too unimportant to go into it just so happens that I start each column of my primes between squares of twin primes at row 5,536 or thereabouts, so I don't even get the full 65,536 numbers that I could otherwise get in each of columns)!


Between (4,584,696,461,808,572,489)^2=21,019,441,646,920,043,379,214,312,327,967,655,121
[21.019441646920043379214312327967655121 undecillion or 2.1019441646920043379214312327967655121x10^37, a 38 digit number] and (4,584,696,461,808,572,491)^2 =21,019,441,646,920,043,397,553,098,175,201,945,081 [21.019441646920043397553098175201945081 undecillion or 2.1019441646920043397553098175201945081x10^37, a 38 digit number] there are at least 940 twin primes between (4,584,696,461,808,572,489)^2 =21,019,441,646,920,043,379,214,312,327,967,655,121 and
21,019,441,646,920,043,379,214,312,327,972,886,863 (with 18,338,785,847,234,289,960 -
5,231,742 = 18,338,785,847,229,058,218 [18.338785847229058218 quintillion or 1.8338785847229058218x10^19, a 20 digit number] in the range to spare)!!!


At this point, a little explanation of terminology may be in order! The issue is how to express large numbers in English! John Conway and Richard Guy have a very good explanation of how we should go about doing this for numbers as large as you like in their superb book The Book of Numbers. Among other things, Conway and Guy point out that what it really all boils down to is coming up with reasonable names for the Nth zillion numbers that are powers of 10 that go like 10^(3N+3), according to the American naming system and not the British naming system, which uses 10^6N instead! The first few of these are well known and beloved by all: one million (1,000,000=10^6, a 7 digit number) for N=1, one billion (1,000,000,000=10^9, a 10 digit number) for N=2, one trillion (1,000,000,000,000=10^12, a 13 digit number) for N=3, one quadrillion (1,000,000,000,000,000=10^15, a 16 digit number) for N=4, one quintillion (1,000,000,000,000,000,000=10^18, a 19 digit number) for N=5, one sextillion (1,000,000,000,000,000,000,000=10^21, a 22 digit number) for N=6, one septillion (1,000,000,000,000,000,000,000,000=10^24, a 25 digit number) for N=7, one octillion (1,000,000,000,000,000,000,000,000,000=10^27, a 28 digit number) for N=8, one nonillion (1,000,000,000,000,000,000,000,000,000,000=10^30, a 31 digit number) for N=9, and one decillion (1,000,000,000,000,000,000,000,000,000,000,000=10^33, a 34 digit number) for N=10. Notice that the number of triple zero clusters is always one more than the value of N! That's because of the "+3" in the (3N+3) exponent in 10^(3N+3)!


When would you ever have a chance to use such names in everyday conversation? Well, the federal budget is in the trillions (a few times 10^12), for example. The mass of the Earth's atmosphere is roughly 4 quintillion (4x10^18) kilograms. The moon's mass is about 70 sextillion (7x10^22) kilograms. Avogadro's number is 602.214179(30) sextillion (6.02214179(30)x10^23), which is the number of carbon-12 atoms in 12 grams of pure carbon-12, for example (the "(30)" at the end of the number 6.02214179 reflects a "standard experimental uncertainty" of +/-30 in the last two digits [it understood that the number "(30)" in parentheses is the numerical value of the standard uncertainty, the estimated standard deviation, where the N data points are assumed to be adequately characterized by a Gaussian or normal probability distribution that looks like a Bell curve when plotted out, centered on the average or mean value X_average=Sum from i=1 to i=N of (X_i)/N, with a spread about the average value given by s=the square root of the Sum from i=1 to i=N of {(X_i-X_average)^2}/(N-1), the variance normalized by one less than the number N of data points {for exceedingly obscure reasons related to something called the "Student's t-distribution" that I won't go into, which is a welcome relief to all concerned!}] referred to the corresponding last digits of the quoted result--this implies that it is believed with an approximate level of confidence of 68.27% that the "true" value of Avogadro's number probably lies between 6.012214149x10^23 and 6.012214209x10^23, that it is believed with an approximate level of confidence of 95% that the "true" value of Avogadro's number probably lies between 6.012214119x10^23 and 6.012214239x10^23 [from an "expanded" experimental uncertainty of about +/-60 in the last two digits that may readily obtained by multiplying the quoted value of the "standard experimental uncertainty" by 1.960, which I've conveniently rounded up to 2.000, keeping 3 significant digits in the rounding and technically boosting my level of confidence from 95% to 95.45%, as may be confirmed here, at page 82, Table G.1], and that it is believed with an approximate level of confidence of 99% that the "true" value of Avogadro's number probably lies between 6.012214089x10^23 and 6.012214269x10^23 [from an "expanded" experimental uncertainty of about +/-90 in the last two digits that may readily obtained by multiplying the quoted value of the "standard experimental uncertainty" by 2.576, which I've conveniently rounded up to 3.000, keeping 3 significant digits in the rounding and technically boosting my level of confidence from 99% to 99.73%]). As pointed out in the marveously useful book Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin, if you had an Avogadro's number of fairly fat cats (at 10 kilograms each!), they would have a mass of just about 6 septillion (6x10^24) kilograms, which happens to be the mass of the entire Earth! The mass of Jupiter is in the ballpark of one octillion (10^27) kilograms, while the mass of our Sun is approximately 2 nonillion (2x10^30) kilograms or 2 decillion (2x10^33) grams! There are in the neighborhood of 100 billion (10^11) stars in the Milky Way galaxy so it has a mass of 200 duodecillion (2x10^41) kilograms or 200 tredecillion (2x10^44) grams. There are on the order of 100 billion (10^11) galaxies in the whole known Universe, as far as we know, so that the whole known Universe should have a mass of about 20 sedecillion (2x10^52) kilograms, made up predominantly of hydrogen-1 (otherwise known as a proton plus an electron) and helium-4 (otherwise known as an alpha particle plus two electrons), 75% hydrogen-1 (by mass!) and 25% helium-4 (by mass!), corresponding to 15 sedecillion (1.5x10^52) kilograms of hydrogen (7.5 septedecillion moles of molecular hydrogen H_2 or 0.75x10^55 moles of H_2) and 5 sedecillion (0.5x10^52) kilograms of helium-4 (1.25 septedecillion moles of helium-4 or 0.125x10^55 moles of He-4; as the names suggest, helium-4 is almost four times as massive as hydrogen-1, so while there are only one-fourth as many helium-4's as there are hydrogen-1's, each helium-4 has four times the mass of each hydrogen-1, which would lead to exact mass equality for helium-4 and hydrogen-1 were it not for the binding energy of the two protons and the two neutrons that constitute the helium-4 nucleus, which is an alpha particle, the binding energy corresponding to the energy released when four protons fuse together to make the alpha particle as takes place in the thermonuclear reactions at the center of the Sun, for example, in strict accord with Einstein's justifiably famous "E=mc^2" equation, "E" being the energy released when a rest mass "m" is convereted to pure energy, the constant of proportionality being none other than "c" the speed of light in an absolute vacuum, 2.99792458x10^8 meters per second by definition, two-hundred ninety-nine million, seven-hundred ninety-two thousand, four hundred fifty-eight meters per second--the solar power density at one Astronomical Unit or AU, defined as the mean distance from the center of the Earth to the center of the Sun, 15 trillion (1.5x10^13) centimeters, is 1.4 kilowatts per square meter, meaning that the total luminosity of our Sun is 1.4 kilowatts per square meter times the surface area of a sphere cented at the center of the Sun having a radius of 1 AU, (4)x(pi)x(1.5x10^11 meters)^2=(4)x(22/7)x(9/4)x10^22 square meters=2.8x10^23 square meters or two-hundred eighty sextillion square meters, yielding a total luminosity L=(1.4x10^3 watts per square meter)x(2.8x10^23 square meters)=4x10^26 watts(!), which is a lot of watts, 400 septillion of them, which comes about when 4 billion (4x10^9) kilograms of hydrogen-1 rest mass is converted into pure energy by thermonuclear fusion processes at the center of our Sun every second, since E=mc^2=(4x10^9 kilograms)x(3x10^8 meters per second)^2=(4x10^9 kilograms)x(9x10^16 meters squared per second squared)=4x10^26 Joules (400 septillion Joules) every second is 4x10^26 watts(!!), 400 septillion of them, just what the good Dr. Einstein ordered!!!)--WOW, these have to be two of the longest parentheticals (at around 30 lines each!) ever to appear in a single (very long) paragraph in a blog! Could be the effect of the notorious "chemo brain" of which I've heard!


Well, now that we've gotten the swing of this number-naming thing, we can usefully apply our newfound skills to the numbers, prime and otherwise that occur in my investigations into Furlong's Conjecture. For example, Factorizer investigated the occurrence of twin primes, also known as prime pairs, between the squares of the twin primes 46,271 (46.271 thousand, also known as forty-six thousand, two-hundred seventy-one or 4.6271x10^4, 5 digit number) and 46,273 (46.273 thousand, also known as forty-six thousand, two-hundred seventy-three or 4.6273x10^4, a 5 digit number), or in other words (or numbers!), between 2,141,005,441=46,271^2 [2.141005411 billion, also known as two billion, one-hundred forty-one million, five thousand, four-hundred eleven or 2.141005411x10^9, a 10 digit number] through
2,141,190,529=46,273^2 [2.141190529 billion, also known as two billion, one-hundred forty-one million, one-hundred ninety thousand, four-hundred eleven 2.141190529x10^9, a 10 digit number]. I would bet any amount of money that this is the very first time in the long stretch of human history that either of the prime numbers 46,271 and 46,273 have ever had their proper English names written down! Similarly, my number theory kluge in Excel investigated the occurrence of twin primes, also known as prime pairs, between the squares of the twin primes 2,141,190,431 (2.141190431 billion, also known as two billion, one-hundred forty-one million, one-hundred ninety thousand, four-hundred thirty-one or 2.141190431x10^9, a 10 digit number) and 2,141,190,433 (2.141190433 billion, also known as two billion, one-hundred forty-one million, one-hundred ninety thousand, four-hundred thirty-three or 2.141190433x10^9, a 10 digit number), or in other words (or numbers!), between (2,141,190,431)^2=4,584,696,461,805,965,761 [4.584696461805965761 quintillion, also known as four quintillion, five-hundred eighty-four quadrillion, six-hundred ninety-six trillion, four-hundred sixty-one billion, eight-hundred five million, nine-hundred sixty-five thousand, seven-hundred sixty-one or 4.584696461805965761x10^18, a 19 digit number] and
(2,141,190,433)^2=4,584,696,470,370,727,489 [4.584696470370727489 quintillion, also known as four quintillion, five-hundred eighty-four quadrillion, six-hundred ninety-six trillion, four-hundred seventy billion, three-hundred seventy million, seven-hundred twenty-seven thousand, four-hundred eighty-nine or 4.584696470370727489x10^18, a 19 digit number]. Again, I would wager any amount of money that this is the very first time in the long stretch of human history that either of the prime numbers 2,141,190,431 and 2,141,190,433 have ever had their proper English names written down! You all are witnesses to a moment in time never before seen! Which is, of course, true of every moment in time, when you come to think about it, at least when "aided" by "chemo brain!"


Likewise, my Excel number theory kluge investigated the occurrence of twin primes, also known as prime pairs, between the squares of the twin primes 4,584,696,461,808,572,489 (4.584696461808572489 quintillion or 4.584696461808572489x10^18, a 19 digit number, also known as four quintillion, five-hundred eighty-four quadrillion, six-hundred ninety-six trillion, four-hundred sixty-one billion, eight-hundred eight million, five-hundred seventy-two thousand, four-hundred eighty-nine) and 4,584,696,461,808,572,491 (4.584696461808572491 quadrillion or 4.584696461808572491x10^18, a 19 digit number, also known as four quintillion, five-hundred eighty-four quadrillion, six-hundred ninety-six trillion, four-hundred sixty-one billion, eight-hundred eight million, five-hundred seventy-two thousand, four-hundred ninety-one), or in other words (or numbers!), found, between (4,584,696,461,808,572,489)^2=21,019,441,646,920,043,379,214,312,327,967,655,121
[21.019441646920043379214312327967655121 undecillion or 2.1019441646920043379214312327967655121x10^37, a 38 digit number, also known as twenty-one undecillion, nineteen decillion, four-hundred forty-one nonillion, six-hundred forty-six octillion, nine-hundred twenty septillion, forty-three sextillion, three-hundred seventy-nine quintillion, two-hundred fourteen quadrillion, three-hundred twelve trillion, three-hundred twenty-seven billion, nine-hundred sixty-seven million, six-hundred fifty-five thousand, one-hundred twenty-one] and (4,584,696,461,808,572,491)^2 =21,019,441,646,920,043,397,553,098,175,201,945,081 [21.019441646920043397553098175201945081
undecillion or 2.1019441646920043397553098175201945081x10^37, a 38 digit number, also known as twenty-one undecillion, nineteen decillion, four-hundred forty-one nonillion, six-hundred forty-six octillion, nine-hundred twenty septillion, forty-three sextillion, three-hundred ninety-seven quintillion, five-hundred fifty-three quadrillion, ninety-eight trillion, one-hundred seventy-five billion, two-hundred one million, nine-hundred forty-five thousand, eighty-one].


Last, but certainly not least by any stretch of the imagination(!), between (21,019,441,646,920,043,379,214,312,327,972,877,051)^2 =
441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,362,456,601 [441.816927148276785559214254431324696206279105710628344677315905110362456601 tresvigintillion {because there are 24 clusters of three numbers in this leviathan number, the appropriate prefix according to Conway and Guy is related to 23} or 4.41816927148276785559214254431324696206279105710628344677315905110362456601x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-four tredecillion, six-hundred ninety-six duodecillion, two-hundred six undecillion, two-hundred seventy-nine decillion, one-hundred five nonillion, seven-hundred ten octillion, six-hundred twenty-eight septillion, three-hundred forty-four sextillion, six-hundred seventy-seven quintillion, three-hundred fifteen quadrillion, nine-hundred five trillion, one-hundred ten billion, three-hundred sixty-two million, four-hundred fifty-six thousand, six-hundred one] and (21,019,441,646,920,043,379,214,312,327,972,877,053)^2 =
441,816,927,148,276,785,559,214,254,431,325,087,504,204,804,774,155,892,130,954,202,653,528,276,881 [441.816927148276785559214254431325087504204804774155892130954202653528276881 tresvigintillion or 441.816927148276785559214254431325087504204804774155892130954202653528276881x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-five tredecillion, eighty-seven duodecillion, five-hundred four undecillion, two-hundred four decillion, eight-hundred four nonillion, seven-hundred seventy-four octillion, one-hundred fifty-five septillion, eight-hundred ninety-two sextillion, one-hundred thirty quintillion, five-hundred fifty-four quadrillion, two-hundred two trillion, six-hundred fifty-three billion, five-hundred twenty-eight million, two-hundred seventy-six thousand, eight-hundred eighty-one] there are at least 459 twin primes between (21,019,441,646,920,043,379,214,312,327,972,877,051)^2 =
441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,362,456,601 [441.816927148276785559214254431324696206279105710628344677315905110362456601 tresvigintillion or 4.41816927148276785559214254431324696206279105710628344677315905110362456601x10^74, a 75 digit number] and
441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,372,940,363 [441.816927148276785559214254431324696206279105710628344677315905110362456601 tresvigintillion] (with 391,297,925,699,063,527,547,453,638,297,543,165,820,280 - 10,483,762 =
391,297,925,699,063,527,547,453,638,297,543,155,336,518 [391.297925699063527547453638297543155336518 duodecillion or 3.91297925699063527547453638297543155336518x10^41, a 42 digit number, also known as three-hundred ninety-one duodecillion, two-hundred ninety-seven undecillion, nine-hundred twenty-five decillion, six-hundred ninety-nine nonillion, sixty-three octillion, five-hundred twenty-seven septillion, five-hundred forty-seven sextillion, four-hundred fifty-three quintillion, six-hundred thirty-eight quadrillion, two-hundred ninety-seven trillion, five-hundred forty-three billion, one-hundred fifty-five million, three-hundred thirty-six thousand, five-hundred eighteen] in the range to spare)!!! Thus, my number theory kluge in Excel further investigated the occurrence of twin primes, also known as prime pairs, between the squares of the twin primes 21,019,441,646,920,043,379,214,312,327,972,877,051 (21.019441646920043379214312327972877051 undecillion or 2.1019441646920043379214312327972877051x10^37, a 38 digit number, also known as twenty-one undecillion, nineteen decillion, four-hundred forty-one nonillion, six-hundred forty-six octillion, nine-hundred twenty septillion, forty-three sextillion, three-hundred seventy-nine quintillion, two-hundred fourteen quadrillion, three-hundred twelve trillion, three-hundred twenty-seven billion, nine-hundred seventy-two million, eight-hundred seventy-seven thousand, fifty-one, named here in English for the first time ever!) and 21,019,441,646,920,043,379,214,312,327,972,877,053 (21.019441646920043379214312327972877053 undecillion 2.1019441646920043379214312327972877053x10^37, a 38 digit number, also known as twenty-one undecillion, nineteen decillion, four-hundred forty-one nonillion, six-hundred forty-six octillion, nine-hundred twenty septillion, forty-three sextillion, three-hundred seventy-nine quintillion, two-hundred fourteen quadrillion, three-hundred twelve trillion, three-hundred twenty-seven billion, nine-hundred seventy-two million, eight-hundred seventy-seven thousand, fifty-three, also named here in English for the first time ever!), or in other words (or numbers!), between (21,019,441,646,920,043,379,214,312,327,972,877,051)^2 =

441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,362,456,601 [441.816927148276785559214254431324696206279105710628344677315905110362456601 tresvigintillion or 4.41816927148276785559214254431324696206279105710628344677315905110362456601x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-four tredecillion, six-hundred ninety-six duodecillion, two-hundred six undecillion, two-hundred seventy-nine decillion, one-hundred five nonillion, seven-hundred ten octillion, six-hundred twenty-eight septillion, three-hundred forty-four sextillion, six-hundred seventy-seven quintillion, three-hundred fifteen quadrillion, nine-hundred five trillion, one-hundred ten billion, three-hundred sixty-two million, four-hundred fifty-six thousand, six-hundred one] and (21,019,441,646,920,043,379,214,312,327,972,877,053)^2 =

441,816,927,148,276,785,559,214,254,431,325,087,504,204,804,774,155,892,130,954,202,653,528,276,881 [441.816927148276785559214254431325087504204804774155892130954202653528276881 tresvigintillion or 441.816927148276785559214254431325087504204804774155892130954202653528276881x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-five tredecillion, eighty-seven duodecillion, five-hundred four undecillion, two-hundred four decillion, eight-hundred four nonillion, seven-hundred seventy-four octillion, one-hundred fifty-five septillion, eight-hundred ninety-two sextillion, one-hundred thirty quintillion, five-hundred fifty-four quadrillion, two-hundred two trillion, six-hundred fifty-three billion, five-hundred twenty-eight million, two-hundred seventy-six thousand, eight-hundred eighty-one].  Finally, for the sake of completeness, the two largest twin primes found to date in my investigations of Furlong's Conjecture:

441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,372,931,057 [441.816927148276785559214254431324696206279105710628344677315905110372931057 tresvigintillion or 4.41816927148276785559214254431324696206279105710628344677315905110372931057x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-four tredecillion, six-hundred ninety-six duodecillion, two-hundred six undecillion, two-hundred seventy-nine decillion, one-hundred five nonillion, seven-hundred ten octillion, six-hundred twenty-eight septillion, three-hundred forty-four sextillion, six-hundred seventy-seven quintillion, three-hundred fifteen quadrillion, nine-hundred five trillion, one-hundred ten billion, three-hundred seventy-two million, nine-hundred thirty-one thousand, fifty-seven, named here in English for the first time ever!] and 

441,816,927,148,276,785,559,214,254,431,324,696,206,279,105,710,628,344,677,315,905,110,372,931,059 [441.816927148276785559214254431324696206279105710628344677315905110372931059 tresvigintillion or 441.816927148276785559214254431324696206279105710628344677315905110372931059x10^74, a 75 digit number, also known as four-hundred forty-one tresvigintillion, eight-hundred sixteen duovigintillion, nine-hundred twenty-seven unvigintillion, one-hundred forty-eight vigintillion, two-hundred seventy-six novendecillion, seven-hundred eight-five octodecillion, five-hundred fifty-nine septendecillion, two-hundred fourteen sedecillion, two-hundred fifty-four quinquadecillion, four-hundred thirty-one quattuordecillion, three-hundred twenty-four tredecillion, six-hundred ninety-six duodecillion, two-hundred six undecillion, two-hundred seventy-nine decillion, one-hundred five nonillion, seven-hundred ten octillion, six-hundred twenty-eight septillion, three-hundred forty-four sextillion, six-hundred seventy-seven quintillion, three-hundred fifteen quadrillion, nine-hundred five trillion, one-hundred ten billion, three-hundred seventy-two million, nine-hundred thirty-one thousand, fifty-nine, also named here in English for the first time ever!]

My Excel kluge number theory program is supposed to be able to handle numbers up to 250 digits in length, so all that remains to be done is to square these last two twin primes, generating a range of numbers with about 150 digits each.  Based on the trends I've observed up to now, I expect to find around 250 or so twin primes in the first 60,000 or so of this range.  Furlong's Conjecture appears to be in good health, too!

An Important CT Scan Today!

This evening sometime around 6:00PM, hopefully, I will have a CT scan that will show whether or not the 4 rounds of chemotherapy I've had have had an effect on the tumors in my abdominal cavity, both the primary non-carcinoid, mucinous appendiceal adenocarcinoma in and around what's left of my appendix and any and all metastatic nodules on and/or in my peritoneum! The CT scans (technically, there are 2 CT scans, one of my chest and the other of my abdomen/pelvis, but they'll do them both during the same session) will also help determine whether any rogue cells have escaped from my abdominal cavity to anywhere else in my body that such cells are likely to go to (apparently adenocarcinomas from the gut don't often metastasize to the brain or toes, for example)! We're fervently praying and hoping for a good report so we can plan and schedule HIPEC surgery very soon! The sooner these cancer cells are excised from my body and/or killed dead as little doornails, the better! Stay tuned and thanks so much again for all your many wonderful prayers and best wishes and love--I don't know what I would do without all of you! Thank God I have you all on my side! We'll whip this impertinent appendix cancer sooner rather than later! May God bless you all!

Furlong's Conjecture

This past Saturday, I re-entered the "prime" of my life, I turned 53, by the grace of God! As everyone knows, a prime number is a whole number (integer, conventionally denoted as p, for "prime") greater than 1 that has 2 and only 2 distinct whole number divisors, whole numbers that divide into another whole number without leaving any non-zero remainder, namely 1 and itself, p. Indeed, p divided by 1 equals p, and p divided by p equals 1. The first prime number p_1 is 2, which is the unique even prime number (every even number greater than 2 is divisible by 2, in addition to being divisible by 1 and itself, so it cannot be prime)! The next prime number p_2 is 3, since 3 is not evenly divisible by 2. The first composite number, a number greater than 1 that is not prime, is 4, which is evenly divisible by 2 exactly twice. The third prime number p_3 is 5, the second composite number is 6 (which also happens to be the first perfect number, a number that is equal to the sum of all its proper or aliquot divisors, all its divisors that are strictly less than the number itself: the proper divisors of 6 are 1, 2, and 3, and 1+2+3=6), the fourth prime number p_4 is 7, the third composite number is 8, which is evenly divisible by 2 exactly thrice, the fourth composite number is 9, which is (oddly) divisible by 3 exactly twice, and the fifth composite number is 10, which is evenly divisible by 2 exactly once and by 5 exactly once. One can proceed similarly forever!

There happen to be 4 prime numbers less than 10, 25 prime numbers less than 100, 168 prime numbers less than 1000, 1229 prime numbers less than 10000, 9592 prime numbers less than 100000, and 78498 prime numbers less than 1000000, for example! The first 25 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Note that there is one unique pair of neighboring prime numbers, 2 and 3. There are also a fair number of "twin primes" separated by one and only one composite number, such as 3 and 5, 5 and 7, and 11 and 13, for example. It is not known whether there are an unlimited number of twin primes. Euclid cleverly proved centuries ago that there are an infinite number of prime numbers. Assume to the contrary that there are only a finite number of prime numbers, p_1, p_2, p_3, ..., p_n, where p_n is the "largest known prime number." Multiply all of the known primes together and then add 1, forming N=p_n#+1, where p_n# is "p_n primorial", the product of all the prime numbers less than or equal to p_n. Since N is (obviously) greater tha 1, N either is prime or composite. If N is prime, then since N is evidently (much, much) larger than p_n, the so-called "largest known prime," we have demonstrated that there is always at least one more prime number than we thought there were! If N is composite and not prime then N must necessarily have one or more prime divisors that are less than N. However, clearly none of the "known" prime numbers, p_1, p_2, p_3, ..., p_n, are able to divide N without leaving a remainder of 1, so there must exist at least one more prime number p that is greater than the so-called "largest prime number p_n, implying once again that our original assumption that there are only a finite number of prime numbers is wrong and there must therefore be an infinite or unlimited number of prime numbers!

Brocard's conjecture is that there are at least 4 prime numbers between the squares of successive odd prime numbers. I'm pleased to make "Furlong's conjecture," which necessarily includes Brocard's conjecture, but is much more restrictive: there are at least 2 twin primes between the squares of successive odd prime numbers. I have absolutely no idea of how to go about proving my conjecture! I have been able to verify the validity of my conjecture, by judicious sampling, for prime numbers up into the billions (and beyond)! I haven't found a counter-example, yet, but I'll keep looking and be sure to let you all know the outcome!

Arms and the Man, Four Rounds of Chemo Down So Far!

I'm pleased to report that my left arm is healing quite well!  We went in to see the orthopedist at M.D. Anderson Cancer Center on Monday, February 7, 2011, and the x-ray showed new bone being formed to knit together my left humerus across its surgical neck!  In about 4 weeks, I'll be able to start any needed physical therapy and stop wearing a sling!

I'm also pleased to report that I've survived a third and a fourth round of chemotherapy, with hardly any side effects worth reporting!  Hopefully, the chemo treatments are affecting the tumors much more than they are affecting me!  The neuropathy caused by the oxaliplatin part of my FOLFOX regimen does seem to be getting worse with each treatment, although the effects wear off over the course of the two weeks of each chemo treatment.  The numbness and tingling in my fingers and toes and the sensitivity to cold is somewhat annoying, of course, but the worst part, for me at least, is the weird feeling in your throat whenever you try to drink iced drinks or cold liquids.  It's not exactly like nurse Ida explained, that drinking cold beverages feels just like swallowing broken shards of glass, but it is very unpleasant, nevertheless!  Especially to someone like me who is hopelessly addicted to iced quad espressos from Starbucks!  Fortunately, room temperature drinks and hot beverages are fine!  If I have to, I may switch to a hot Venti Americano for a few days!

We are scheduled to meet with my colorectal oncologist, Dr. Imad Shureiqi, this coming Friday, February 25, 2011.  I think the plan is to allow this most recent (fourth) round of chemo to run it's course and then get another CT scan to ascertain whether or not the metastatic non-carcinoid, mucinous appendiceal adenocarcinoma has responded to the chemotherapy.  Hopefully, all the tumors, from the primary tumor in the appendix (or what's left of my appendix) to the metastatic nodules on my peritoneum, will have stopped growing and will have actively shrunk in size, or even better, will have died off altogether!

If so, then we will meet again with my surgical oncologist, Dr. Paul Mansfield, and discuss potential surgical options.  Since my appendix cancer is metastatic, as shown by the needle biopsy performed on one of the peritoneal nodules near the surface of my skin, the aggressive surgery that includes hyperthermal intraperitoneal chemotherapy (HIPEC) may well be in my future!  After my appendix and the right half of my colon and any involved lymph nodes and any and all peritoneal nodules have been removed from my abdominal cavity, heated chemotherapy chemicals are introduced into my abdominal cavity, bathing all the tissues directly with the chemo agents heated to about 40 degrees Centigrade (which is 104 degrees Fahrenheit).  Apparently, during the warm chemo bath, my body will be gently shaken for about 90 minutes (I will be anesthetized, of course, so I probably won't feel the gentle shaking!), insuring that all potentially affected portions within my peritoneum will be adequately exposed directly to the warm chemo.  This direct exposure of the tissues to the warm chemo is apparently much more effective than chemo delivered through my veins.  Roughly one-third of the patients receiving the HIPEC surgery treatment have complete remission of their cancers with no recurrence of the disease, or so I'm told.  Those are pretty good odds!  Much better than winning the lottery, for example!  After I've recovered adequately from the surgery, which could take up to six weeks or two months, especially after the HIPEC treatment, then I will continue with another eight rounds of the FOLFOX chemo treatments, for a grand total of twelve.

Thanks again for all your thoughts and prayers!  They are definitely working and very definitely appreciated!

Two down and two to go (in first round of Chemo)

I am very happy to report that I've survived two infusions of chemotheraphy so far!  The plan is for me to receive chemo every other week for a total of 8 weeks (four infusions in all) and then to wait another fortnight before I have another Computerized Tomography (CT or CAT) scan to see whether the chemo has been effective against my metastatic mucinous (and mutinous, as "Paddy" our iPad "corrected" its spelling appropriately recently) appendiceal adenocarcinoma.

So far, the side effects have been very mild, indeed.  After my most recent infusion this past weekend, the peripheral neuropathy in my fingertips and toes was a little more noticeable, as was the sensitivity to cold liquids that makes drinking iced drinks somewhat unpleasant.  I was warned by Nurse Ida that drinking iced drinks would feel like swallowing broken shards of glass, although it wouldn't really be causing me any physical harm.  When I drank an iced drink, it didn't feel like swallowing shards of glass, but the feeling was definitely unpleasant, almost like it was trying to trigger a gag reflex or something.  Reluctantly, I've decided to stay away from my beloved iced quad espresso from Starbucks until such sensations abate!  I fervently hope and pray that my tumors are being affected much more than I am!

Chemo-sabe?

I'm very pleased to report that I appear to have survived my very first round of FOLFOX chemotherapy and am not too much worse for the wear! Thank God I was spared the ravages of the many side effects of these wonder chemicals! The portable battery-operated pump and my Bard Power Port worked flawlessly to deliver 5-flurouracil into a catheter in my jugular vein at the stately and quite sedate pace of 5.2 ml/hour for 46 straight hours! Miraculously, I was even able to sleep on my back, placating my left arm in it's sling as well as the portable battery-operated pump slung in it's own fanny pack under my right arm! And I'm also getting used to my new CPAP machine, nasal mask, humidifier, and chinstrap. Somewhat surprising that I was able to get any sleep at all!

I'm also very pleased to report that I'm now able to update my blog using our new, beloved iPad, which was given to us by some wonderful and overly generous friends of ours! Thanks so much you all (and you know who you are!), you all shouldn't have (but we're so very glad you did!)--you all have warmed the chemo-basted cockles of my heart!

I Never Met a Metastasis That I Liked!

The start of my chemotherapy has been delayed a bit, and the nature of the mix of therapies that will be used has been changed, too, all because my stupid right foot hit an uneven place on the sidewalk outside of our church (Grace Episcopal) the day after Christmas 2010, making me lose my balance and fall over onto the grass on my left shoulder and left arm with sufficient force to fracture the "surgical neck" of my left humerus! I was supposed to start my first round of FOLFOX spiked with Avastin last Friday, New Year's Eve. Now, I'm scheduled to start my first round of FOLFOX without the Avastin this coming Friday, January 7, 2011 (the day after my Father's 80th birthday, which is also known as Epiphany!)--apparently, the Avastin would completely screw up the natural healing processes knitting my left humerus together again as long as I immobilize my left arm in a sling. The Avastin helps prevent the formation of some of the blood vessels that are needed to supply life-giving blood to both growing tumors and healing wounds! FOLFOX will also slow the bone healing somewhat, but not nearly as much as the Avastin would. Perhaps, after my humerus is all healed up, which could take up to 6 or 8 weeks even under normal circumstances, we can add the Avastin back into the mix for a further round of chemo, if needed. Most of the heavy lifting in the tumor-killing achieved by the chemo is done by the FOLFOX, with the Avastin adding some "icing to the cake," enhancing the effectiveness of FOLFOX.

Today, we got the results back from last week's needle biopsy.  It's now "official"--the appendiceal adenocarcinoma that originated in my "Benedict Arnold" appendix has metastasized!  Cells that were consistent with the appendiceal adenocarcinoma cells found in the biopsies from my colonoscopy (performed at Memorial Hermann Hospital on November 29, 2010) -- were also found in one of the 1 cubic centimeter (1 cc = 1 milliliter = 1 ml) "nodules" identified in my latest computerized tomography (CT) x-ray scan from December 13, 2010! As I wrote (on Skype) to the Contessa (yes, the Countess herself, the very same woman I was briefly engaged to for a few months over 26 years ago, when I was in graduate school at the Rockefeller University and had gone to a physics summer school in Erice, Sicily, despite the fact that I had no money -- "If you had no money, how could you want to get married?" -- and the fact that she had trouble remembering my name -- "I'm so sorry I forgot your name!"!):

Francesca, Happy New Year to you all! We met with my GI (colorectal) oncologist, Dr. Imad  Shureiqi, to get the results from last week's needle biopsy and he confirmed what I'd expected for a while (ever since we learned from the CT scan that there were 1 cc "nodules" on my peritoneum), that the appendix cancer had metastasized and spread into at least the peritoneum! Bummer! But, at least we know for sure what we're up against, so we can go after it with everything at our disposal! I finally start my chemo treatments this coming Friday morning, at 8:30AM! I'll go in every other week for a total of 4 treatments in 8 weeks and then we'll take another CT scan to see whether or not the chemo has reduced the cancer any! If so, we might then opt for surgery to cut out every tumor they can find in my gut and then apply a warm chemo bath directly onto my peritoneum! If not, we can change to a different type of chemo until we find one that kills the tumors more effectively than it kills me! It's a very good sign that there don't appear to be any tumors anywhere outside of my peritoneum--all my other vital organs (heart, brain, liver, lungs, kidneys, pancreas, spleen, stomach, etc.) are tumor-free! So, I'm still very optimistic about my prospects and my prognosis--I'm relatively young (52.9 years old!), in relatively good health (other than my appendix cancer and my left arm!), we've fortuitously discovered the tumor fairly early on (thanks to my mysterious bleeding in November!), I'm at one of the best cancer hospitals in the world where many 100's of
people have been successfully treated for very rare appendix cancers, and I have so many wonderful friends and family members who are all praying fervently for my healing and wholeness and well-being--I can actually feel myself being lifted up by all the prayers and genuine, sincere concerns of others--lots of good karma! And, if worse comes to worst, at least Caroline and I had the good sense (actually, it was mostly Caroline's good sense!) to take out a large life insurance policy on me--at least she will be provided for, to some degree (to her credit, she tells me that she'd rather have me, with all my faults and failings, than the money)! Nobody lives forever here on good old planet Earth and we all have to go at some time or other and I've had a very good and very blessed life so far, already having lived to a ripe old age compared to most human beings who have lived on Earth for the past 40,000 years or so! Not that I'm at all ready to die and be no more (I can't even begin to get my mind around that concept of nothingness!), I'm quite happy to live as long as possible, continuing to love and learn and suck the marrow out of the bones of life here on Earth! But, I am at peace at the core of my being, quite convinced, in the very marrow of my bones, that the Universe is profoundly empty of insignificance and meaninglessness--the Buddha was right that we are all living in a state of perfection right now, just as we are! I do find myself appreciating each passing moment more than I ever did before--how awesomely precious is each inspirational breath and each beat of our hearts!--I offer up quick prayers of thanksgiving for all of
them! I freely admit that I love life more than I can ever know! I have no recollection of who or what or where or when or why I was before I was ever born and I likewise have no idea or conception of who or what or where or when or why I will be after I am no more (although I sincerely doubt whether 70 virgins will be involved, I believe, and am extremely encouraged and heartened by, the words of Jesus on the cross to the "penitent thief," according to Luke 23:43, "Truly, I say to you, today you will be with me in paradise!"!)! To some extent, I will live on in the memories and hearts of those who have known and loved me, whom I also have known and loved--I don't think any amount of love is ever lost or wasted or for naught! Some of my genes will undoubtedly live on and be passed down from generation to generation through my blood relative nieces and nephews (since I share a fair number of my genes with my blood sister and blood brother, all of us having descended from the same blood parents and blood grandparents, etc., etc.!)! Ineluctably and indescribably, subatomic quantum entanglements will always bind every bit of my mass-energy with that of everyone else and everything else in the Universe! Who knows, maybe even a few of my original thoughts and creations will survive into the mists of the ages! Whatever! Ciao for niao! Randall

Will Rogers may well have never met a man he didn't like, but I've certainly met a metastatic appendiceal adenocarcinoma that I don't like at all! Please pray for my wife, Caroline--she has a big job interview coming up at the University of Houston this coming Friday afternoon!