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 Showing results 1 to 25 of 1000 Search took 0.27 seconds. Search: Posts Made By: paulunderwood
 Forum: Miscellaneous Math 2021-12-06, 01:14 Replies: 7 Views: 70 Posted By paulunderwood To fool these "semi Euler" PRP tests, find a... To fool these "semi Euler" PRP tests, find a prime number with kronecker(2,n)==-1 and kronecker(-1,n)==-1 respectively.... The first: T(q)={Wq=3*2^2-1;S0=2^3;S=S0;print("q=...
 Forum: Miscellaneous Math 2021-12-05, 22:42 Replies: 7 Views: 70 Posted By paulunderwood Nor Riesel ... Nor Riesel q=4;Wq=557*2^q-1;S0=2^557;print(q," ",Wq);print(Mod(S0,Wq));S=S0;for(i=1,q,S=Mod(S^2,Wq);print(S)) 4 8911 ...
 Forum: Miscellaneous Math 2021-12-05, 22:19 Replies: 7 Views: 70 Posted By paulunderwood q=4;Wq=35*2^q+1;S0=2^35;print(q,"... q=4;Wq=35*2^q+1;S0=2^35;print(q," ",Wq);print(Mod(S0,Wq));S=S0;for(i=1,q,S=Mod(S^2,Wq);print(S));print(S==S0) 4 561 ...
 Forum: Miscellaneous Math 2021-12-05, 21:52 Replies: 7 Views: 70 Posted By paulunderwood q=1;Wq=80*7^1+1;S0=7^80;print(q,"... q=1;Wq=80*7^1+1;S0=7^80;print(q," ",Wq);print(Mod(S0,Wq));S=S0;for(i=1,q,S=Mod(S^7,Wq);print(S));print(S==S0) 1 561 ...
 Forum: Riesel Prime Search 2021-12-03, 22:50 Replies: 74 Views: 28,105 Posted By paulunderwood A slightly smaller one: 69* 2^14977631 - 1... A slightly smaller one: 69* 2^14977631 - 1 (https://primes.utm.edu/primes/page.php?id=133013) :banana:
 2021-11-28, 22:16 Replies: 17 Views: 7,772 Posted By paulunderwood Another way to do it with Pari-GP is... Another way to do it with Pari-GP is 2^89\10^2%10^21 where the infix operator \ gives the quotient.
 Forum: Miscellaneous Math 2021-11-28, 14:42 Replies: 431 Views: 41,132 Posted By paulunderwood Sorry for the confusion. I was just referring to... Sorry for the confusion. I was just referring to Tucker's blunder in general.
 Forum: Miscellaneous Math 2021-11-28, 08:07 Replies: 431 Views: 41,132 Posted By paulunderwood Gender populations are not 50::50. Most forumites... Gender populations are not 50::50. Most forumites here happen to be male. Some people like to identify as non-binary gender. "Dobri" is mainly a man's name. Like your guess at 168Mb for the next...
 2021-11-28, 07:50 Replies: 82 Sticky: Primo reservation thread Views: 26,481 Posted By paulunderwood Welcome back to the fold. I should be... Welcome back to the fold. I should be continuing these shortly into the new year :devil: I can do the Mersenne cofactor Ryan reserved about a year ago too. Ryan?
 2021-11-28, 07:42 Replies: 17 Views: 7,772 Posted By paulunderwood Playing the sleuth, I think I can answer this.... Playing the sleuth, I think I can answer this. Putting "Gleit kommarechnerheizgerät" in to google translate gives "Sliding comma computer heater". The German people often concatenate their written...
 Forum: Hardware 2021-11-27, 21:34 Replies: 224 Views: 37,938 Posted By paulunderwood Formidable power. I had toyed with getting such a... Formidable power. I had toyed with getting such a system. The potential noise put me off. It would draw about 1400w running flat out. One would need a garage or basement to house it. I think it is...
 Forum: Math 2021-11-27, 09:22 Replies: 9 Views: 460 Posted By paulunderwood It is not so great since (3/2)^2-2 = 1/4 which is... It is not so great since (3/2)^2-2 = 1/4 which is already known. Just as (3)^((Mp - 1)/2) == -1 mod Mp for Mersenne primes, we have (-7)^((Wq - 1)/2) == 1 mod Wq for Wagstaff PRPs. The latter can...
 Forum: Math 2021-11-26, 23:49 Replies: 9 Views: 460 Posted By paulunderwood More on the seed 3/2 for Wagstaff numbers. ... More on the seed 3/2 for Wagstaff numbers. Mod(Mod(x,W),x^2-3/2*x+1) is at the heart because S = S0 = 3/2 = x+1/x which leads to the recurrence S=S^2-2 mod W The solution for x is ( 3/2 +-...
 Forum: Math 2021-11-26, 22:38 Replies: 9 Views: 460 Posted By paulunderwood I just found this works for (2/3)^-1 ... I just found this works for (2/3)^-1 wag(q)=W=(2^q+1)/3;S0=S=Mod(3/2,W);for(i=2,q,S=S^2-2);S==S0; So maybe there is some relationship between inverse seeds for Mersenne and Wagstaff. I.e if S0...
 Forum: Miscellaneous Math 2021-11-26, 21:22 Replies: 64 Views: 20,597 Posted By paulunderwood I don't know about what you are driving at, but... I don't know about what you are driving at, but isn't a bit like "Goldbach" -- strong numerical evidence but no proof? Anyway here is an interesting youtube video on prime gaps which sounds...
 2021-11-26, 19:47 Replies: 30 Views: 5,748 Posted By paulunderwood I have done the program with a while loop rather... I have done the program with a while loop rather than a do-while loop. You can strip out the shifted functionality as it makes no difference to timings -- for a random number it does make sense but...
 Forum: Wagstaff PRP Search 2021-11-26, 15:13 Replies: 7 Views: 748 Posted By paulunderwood 4*S = (2^q+4)/3 == 1 mod W. So S = 1/4 mod W... 4*S = (2^q+4)/3 == 1 mod W. So S = 1/4 mod W Therefore S0 = 1/4 S1 = (1/4)^2 - 2 = -31/16 S2 = (-31/16)^2 - 2 = 449/256 .... S_{q-1} = X/4^2^(q-1). This will be X if W is 4-PRP -- aren't...
 Forum: Wagstaff PRP Search 2021-11-26, 05:21 Replies: 7 Views: 748 Posted By paulunderwood This looks promising. Prove it, if you can. ... This looks promising. Prove it, if you can. You might write the code as: wag(q)=W=(2^q+1)/3;S0=S=Mod((2^(q-2)+1)/3,W);for(i=2,q,S=S^2-2);S==S0;
 2021-11-26, 05:05 Replies: 30 Views: 5,748 Posted By paulunderwood Quoting the excellent GMP website documentation: ... Quoting the excellent GMP website documentation: I changed "fdiv" to "cdiv" and all is well with Bernhard's problematic example. :grin: Bernhard should think of these artifacts as a...
 Forum: Linux 2021-11-21, 17:04 Replies: 6 Views: 937 Posted By paulunderwood That's a nice graphical way of doing it, but I am... That's a nice graphical way of doing it, but I am unsure that before copying the OS you can select /dev/sdaX. I don't want the other partitions to be destroyed. It seems to be, after a firmware...
 2021-11-20, 14:01 Replies: 13 Views: 1,599 Posted By paulunderwood The row of data for 9 digits has been added. The... The row of data for 9 digits has been added. The data for 10 digits will take another month of so. I have tried to make the English simpler. So it is worth downloading the latest copy from post #1...
 Forum: Miscellaneous Math 2021-11-16, 23:54 Replies: 0 Views: 81 Posted By paulunderwood 1+1 selfridges test for 1/8 of numbers I was playing around while I waiting for some results to come in... For n=3 mod 4 such that kronecker(-3,n)==-1 and kronecker(-7,n)==-1 test Mod(2,n)^((n-1)/2)==kronecker(2,n) and...
 Forum: Riesel Prime Search 2021-11-16, 18:04 Replies: 101 Views: 27,775 Posted By paulunderwood It is not available for armhf64. Our only hope is... It is not available for armhf64. Our only hope is that somehow Ernst's Mlucas library could do it. Ernst? Pi's etc are much slower than AMD/Intel x86/x64 at crunching mega bit numbers
 Forum: Miscellaneous Math 2021-11-16, 17:33 Replies: 5 Views: 711 Posted By paulunderwood There is nothing "fast" about it. Primo is just... There is nothing "fast" about it. Primo is just as fast. Of course it would be nice to have a 128 core ECPP program, if not more cores! Maybe the Pari-MPI team will make their ECPP software...
 2021-11-14, 00:06 Replies: 56 Views: 9,557 Posted By paulunderwood The same reasoning why a CPAP-11 has yet to be... The same reasoning why a CPAP-11 has yet to be found: https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression#Consecutive_primes_in_arithmetic_progression I found precomputing the primorial...
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