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 Showing results 1 to 25 of 1000 Search took 0.32 seconds. Search: Posts Made By: paulunderwood
 Forum: Hardware 2021-11-27, 21:34 Replies: 224 Views: 37,421 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: 8 Views: 163 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: 8 Views: 163 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: 8 Views: 163 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: 20,391 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: 5,553 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: 362 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: 362 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: 5,553 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: 591 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: 1,239 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: 50 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: 98 Views: 27,402 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: 670 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: 55 Views: 9,203 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...
 2021-11-13, 23:23 Replies: 55 Views: 9,203 Posted By paulunderwood Very nice! Did you use a lot of cycles sieving... Very nice! Did you use a lot of cycles sieving and PRP'ing?
 2021-11-13, 22:47 Replies: 30 Views: 5,553 Posted By paulunderwood In that case you need: void mpz_mod_mp... In that case you need: void mpz_mod_mp (mpz_t r, mpz_t A, mp_bitcnt_t p) { mpz_t a; mpz_init_set(a, A); do { mpz_fdiv_r_2exp(r, a, p); mpz_fdiv_q_2exp(a, a,...
 2021-11-13, 21:50 Replies: 30 Views: 5,553 Posted By paulunderwood Here is my solution written in C #include... Here is my solution written in C #include #include #include void mpz_mod_mp (mpz_t r, mpz_t a, mp_bitcnt_t p) { // assumed that r is initialized and a is...
 2021-11-13, 20:18 Replies: 30 Views: 5,553 Posted By paulunderwood Has it been initialized? Has it been initialized?
 2021-11-13, 20:08 Replies: 30 Views: 5,553 Posted By paulunderwood can you output p and f in that function for us to... can you output p and f in that function for us to see?
 2021-11-13, 19:51 Replies: 30 Views: 5,553 Posted By paulunderwood Without checking the manual that may well be the... Without checking the manual that may well be the case, but mpz_sizeinbase returns an int?
 2021-11-13, 19:24 Replies: 30 Views: 5,553 Posted By paulunderwood It usual for p to be a prime and Mp to be the... It usual for p to be a prime and Mp to be the corresponding Mersenne number. If you have passed in p then why do you need Mp? What is f?
 Forum: MattcAnderson 2021-11-12, 11:08 Replies: 11 Views: 289 Posted By paulunderwood In your opinion. Or can you prove the prime... In your opinion. Or can you prove the prime numbers are platonic (https://en.wikipedia.org/wiki/Theory_of_forms)?
 Forum: MattcAnderson 2021-11-12, 10:09 Replies: 11 Views: 289 Posted By paulunderwood Would you "opinion" still exist when "the closest... Would you "opinion" still exist when "the closest stars burn out and become dark"? Ergo would "1+1=2"?
 Forum: CADO-NFS 2021-11-11, 21:20 Replies: 18 Views: 776 Posted By paulunderwood What are the symptoms? Sometimes all it takes is... What are the symptoms? Sometimes all it takes is a new CR 2032 battery for the mainboard. :smile:
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