From baisley at alumni.rice.edu Wed Dec 24 10:39:48 2014 From: baisley at alumni.rice.edu (Wayne Baisley) Date: Wed, 24 Dec 2014 12:39:48 -0600 Subject: [FoRK] The WEB-DNA Conjecture In-Reply-To: References: <52D3F1D2.5050805@alumni.rice.edu> Message-ID: <549B0874.9010204@alumni.rice.edu> ... or the adjustment to make ... When You?re Halving More Than One I have an updated rendition of the Conjecture, to dispatch a slight flaw in the original. The new constant is 421, to offset one's penalty. https://craptard.wordpress.com/2014/01/09/93/ Cheers, Wayne From greg at bolcer.org Wed Dec 24 11:38:42 2014 From: greg at bolcer.org (Gregory Alan Bolcer) Date: Wed, 24 Dec 2014 11:38:42 -0800 Subject: [FoRK] The WEB-DNA Conjecture In-Reply-To: <549B0874.9010204@alumni.rice.edu> References: <52D3F1D2.5050805@alumni.rice.edu> <549B0874.9010204@alumni.rice.edu> Message-ID: <549B1642.2000604@bolcer.org> Okay, a little blue skying here... I think any factorial, even raised by a power, is not prime. So the speculation is that any nonprime number no matter how large plus that exact prime would be prime? So, using the twin primes conjecture about prime deserts, there are infinitely many pairs of primes that differ by only two. (That also means there are infinitely many pairs of primes that differ by only 421). So, you simply need to prove that for any n!+421, it's bounded (either by 246 {hard} or 2 {Erdos hardest}) by one prime on one side and one prime on the other, so therefore it cannot be prime. My bet is on proving it's not versus proving it always is. Greg On 12/24/2014 10:39 AM, Wayne Baisley wrote: > ... or the adjustment to make ... > > When You?re Halving More Than One > > I have an updated rendition of the Conjecture, to dispatch a slight flaw > in the original. The new constant is 421, to offset one's penalty. > > https://craptard.wordpress.com/2014/01/09/93/ > > Cheers, > Wayne > _______________________________________________ > FoRK mailing list > http://xent.com/mailman/listinfo/fork > -- greg at bolcer.org, http://bolcer.org, c: +1.714.928.5476 From baisley at alumni.rice.edu Wed Dec 24 13:56:17 2014 From: baisley at alumni.rice.edu (Wayne Baisley) Date: Wed, 24 Dec 2014 15:56:17 -0600 Subject: [FoRK] The WEB-DNA Conjecture In-Reply-To: <549B1642.2000604@bolcer.org> References: <52D3F1D2.5050805@alumni.rice.edu> <549B0874.9010204@alumni.rice.edu> <549B1642.2000604@bolcer.org> Message-ID: <549B3681.6090707@alumni.rice.edu> > I think any factorial By definition, not prime. even raised by a power, is not prime. Even more especially not prime. > So the speculation is that any nonprime number no matter how large plus that > exact prime would be prime? My speculation, er conjecture, was that not any, but rather a specific highly non-prime number plus a particular prime number, is prime. But, if you wish to consider a general case, we can do that. > So, using the twin primes conjecture about prime deserts, there are > infinitely many pairs of primes that differ by only two. (That also means > there are infinitely many pairs of primes that differ by only 421). There are exactly 0 pairs of primes that differ by 421. One of any pair of numbers that differs by an odd amount must be even, and therefore not prime. With the possible exception of 2, but 423 is not prime. Anyway, let's pick a slightly different prime, since this case is easier: 431 is a prime number. 3! = 6, is a factorial, and therefore not prime. 6 ^ 6 + 431 = 47,087, which is prime. Roughly the same form as mine. (BTW, 6 ^ 6 - 431 = 47,087, which is not prime. Not that it matters much.) > So, you simply need to prove that for any n!+421, it's bounded (either by 246 > {hard} or 2 {Erdos hardest}) by one prime on one side and one prime on the > other, so therefore it cannot be prime. Of course, my point was not whether my conceit, er conjecture, is actually true. I greatly doubt that it is. It's merely a plausible (of suitably fuzzy values of plaus) framework on which to note that eventually the value n!, or even n becomes too large to actually do anything with, even though it's finite, philosophically. That point comes extremely quickly with n\$. Cheers, Wayne