I encouraged Jens to ask Francois to do ECPP on this worthy target and am delighted to see the endpoints proven. Now Jens has to work out how to enter the two ...
... Let "n" be a Perrin PSP for which M^n==M mod n where Id=[1,0,0;0,1,0;0,0,1] M=[0,1,1;1,0,0;0,1,0] Now I restrict attention to those for which 3^i|n-1. If...
... Matrices have standard cyclotomy, since their eigenvalues do. So subst(polcyclo(k),x,M) with k|n^u-1 should solve your problem, which came from trying to...
... Thanks. The Prime Pages does not record prime gaps so the end points only qualify because ECPP was used. Arbitrary prp's of this size are easy to find so...
... Working modulo n, for the PSP example n=4982970241 we have have for odd 5|n-1: t(5)!=3 g(5)==1 g2(5)==1 but t2(5)==5 [t2(d)==d is not allowed from now on.]...
Paul: If you will write a short self-contained GP test that is 1) passed by every prime 2) failed by every Perrin PSP that I have given you 3) uses only powers...
... A "short self-contained GP test" is beyond me because the program is not short and I cannot program GP very well. ... I think that not every prime will...
Hi, I have run some tests on primes and only a few conform to M^n==M mod n and none were shown to be prime. For the others, the M^(n^6) route was fruitless. So...
Paul: Allowing kronecker, which is very cheap, there is a way to allow all primes to pass and to leave (at present) only S-type PSPs with M^n=M (since no PSP...
I haven't made any progress on the sub-puzzle. I've been working with C with the GMP library and the factoring step has been the roadblock. Looks like it's...
... I was seriously impressed by the ability of Pari-GP to handle 54-digit factorizations, in quantity, on the fly. Of course, there are better dedicated...
... But then I thought of _far_ more scary challenge: Grand-Prix Puzzle: Can anyone _prove_ that there exists a single prime less than 10^6 that is _not_ one...
Here is a demonstration that there are an infinite number of Twin Primes, and a method of finding them. Consider the following twin primes: (5,7) (11,13) (17,...
Milton Brown
miltbrown@...
May 5, 2005 10:12 pm
5828
Milton: Please confine your absurd messages to less discriminating fora. Friends: Please do not feed this infamous troll! David...
Least Twin Primes Past Factorial n, n!, n+1, length, least twin primes past factorial 2 2 3 2 => (5, 7) 3 6 4 4 => (11, 13) 4 24 5 18 => (29, 31) 5 120 6 96 =>...
Milton Brown
miltbrown@...
May 6, 2005 4:20 am
5830
Least Twin Primes Past Factorial n, n!, n+1, length, least twin primes past factorial 2 2 3 2 => (5, 7) 3 6 4 4 => (11, 13) 4 24 5 18 => (29, 31) 5 120 6 96 =>...
Milton Brown
miltbrown@...
May 7, 2005 4:38 am
5831
Hi All, My search for >5000 digit BLS provable CPAP or triplet continues. (without success. I'll get there eventually) Over the past 17 months ,,yI have...
Congrats Ken! This is a big leap over the 2197 digit sequence found by Jim and Hans some three years ago: http://hjem.get2net.dk/jka/math/aprecords.htm#records...
... Just relegated to http://hjem.get2net.dk/jka/math/aprecords.htm#history :-) Big congratulations from me too. ... Factoring a little deeper does the trick,...
Hi Paul, It may be to do with the version of pfgw used. I didn't specift -f at all. As far as switches go I only needed pfgw -t (I used -tc first but found it...
Hi David, Either I've been very unlucky or I didn't calculate it rightas I'm over 3 times what I thought I'd need. Prior to 6*10^9 I sieved +7 to 5*10^6 and...
This has to do with the deeper level that the "tree-factorize" code gives you. Since it was so much faster (if the numbers are of any size), it factors...
http://en.wikinews.org/wiki/200_digit_number_factored says: The number is the largest integer yet factored with a general purpose algorithm. A possibly silly...
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