As everyone knows, binomial coefficients are very smooth, which means that +/-1 terms have a reasonably high prime density. Looking at the top-5000, with a few...
... Cino is going to send us a proof that that there is no integer k such that k^2-7 is the cube of an integer. k^2-17 is the cube of an integer for the...
... http://www.math.harvard.edu/~elkies/hall.html gives this wonderous result: 5853886516781223^3 - 447884928428402042307918^2 = 1641843 which is of a quality...
Hi, PFGW.EXE fails on my Windows 2003 X64 / AMD Opteron system, (unhandled win32 exception) - is this a known issue? So, I thought, no problem, I'll just...
Could someone explain to me why big Sophie Germain primes are described in the form "x * 2^P-1" - eg "2540041185*2^114729-1", when the definition of a...
Hello ! P is here the number p=2540041185*2^114729-1. Not the exponent "114729". ... ___________________________________________________________ Telefonate...
... described ... Sophie GERMAIN primes are primes P such that P is prime and 2*P - 1 is prime too Big primes are not easy to prove primes except when of the...
Hello members! Is it true that: If p mod 4=3 and [2^p MOD (2*p^2+p)] - (2*p+1) = 0 then p and 2p+1 (possible!) Sophie Germain prime pair p,2p+1. We have 1 PRP...
Hello members! Is it true that: * If p mod 4=3 and [2^p MOD (2*p^2+p)] - (2*p+[2]) = 0 then p and 2p+1 (possible!) Sophie Germain prime pair p,2p+1. We have 1...
... Very nice! In brief, No square is congruent to 7 modulo 8. (2*h+1)^3 + 8 = (2*h+3)*(4*h^2+3) != k^2 + 1 since no factor of k^2+1 is congruent to 3 modulo...
Saturday, September 02, 2006 11:58 PM [GMT+1=CET], ... If a = 4m + 3 and a can be write as a = s^3 - t^2, there isn't solutions to that Mordell equation if s =...
Hi, congrats to Larry Soule for the 139,672 digit Near-rep digit prime record: 99*10^139670-1: http://primes.utm.edu/primes/page.php?id=78434 Paul -- recent OU...
Thanks - I started searching at n=60k running on 4-5 machines starting about 3 week ago. I'm not sure how long it will last. I see 7 new NRD entries in the...
... Yes indeed. GIMPS checked the residue, redid the last part of the test, and all looked well. It is currently undergoing an independent verification on a...
... I saw that there was speculation, in another place, that Curtis and Stephen might have had received a second bolt of lightning in Missouri. If that...
A harmless(?) little base-10-curio exercise: Find a pair of distinct titanic NRD primes, with one prime obtained by rotating the other by 180 degrees about an...
... http://www.mersenne.org/prime.htm Lightning strikes twice. On September 4, 2006, in the same room just a few feet away from their last find, Dr. Curtis...
... Indeed, lightning can strike twice: http://www.mersenne.org/prime.htm Lightning strikes twice. On September 4, 2006, in the same room just a few feet away...
George should be able to announce the result of the first verification in about 6 hours. He receives emails from me every half an hour with the status of the...
... Whoops. I claimed to have found 2 titanic pairs below 1400 digits, but each is (Phil please note) a titanic "totally tetradic" near-repunit palindrome. So...
... ************************* I take a day of my computer to found your puzzle but not any number comes ! So it seems to me that if one time you misfound there...
... Thanks for the check with 0 and with 8 . Did you also check the form with 6 <==>9 ? I like this little puzzle because the heuristics say that each of the 3...
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