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 Showing results 1 to 25 of 1000 Search took 0.27 seconds. Search: Posts Made By: paulunderwood
 Forum: Factoring 2021-04-20, 17:42 Replies: 23 Views: 591 Posted By paulunderwood You will probably have to install the ssh server... You will probably have to install the ssh server with sudo apt-get install openssh-server. Debian shuts down after 20 mins after a fresh install and it is necessary to mask power saving. See this...
 Forum: Miscellaneous Math 2021-04-19, 20:26 Replies: 26 Views: 533 Posted By paulunderwood You have described the LL test and a Fermat base... You have described the LL test and a Fermat base 3 PRP test. There are many tricks to speed up computation for Mersenne numbers. :smile:
 Forum: Homework Help 2021-04-19, 11:36 Replies: 9 Views: 174 Posted By paulunderwood https://en.wikipedia.org/wiki/Principia_Mathematic... https://en.wikipedia.org/wiki/Principia_Mathematica A very soporific read!
 Forum: Homework Help 2021-04-18, 14:14 Replies: 9 Views: 174 Posted By paulunderwood (a+b)^2 means A*B where A=B=a+b ... (a+b)^2 means A*B where A=B=a+b (a+b)*(a+b)=a*(a+b)+b*(a+b) with right distribution a*(a+b)+b*(a+b)=a^2+a*b+b*a+b^2 with two applications of left distribution The desired result follows...
 Forum: Homework Help 2021-04-18, 13:15 Replies: 9 Views: 174 Posted By paulunderwood You'll have to use the distributive laws (and... You'll have to use the distributive laws (and rearrange terms using the axiom you mentioned). :smile:
 Forum: Miscellaneous Math 2021-04-15, 11:39 Replies: 9 Views: 227 Posted By paulunderwood No matter how many -- a reasonable number -- MR... No matter how many -- a reasonable number -- MR tests you do there will be counterexamples. 1+1..+1+1 selfridges is a poor test and cryptographically weak. This is one of the reasons why GMP now...
 Forum: Miscellaneous Math 2021-04-09, 19:21 Replies: 35 Views: 687 Posted By paulunderwood Whatever you do with 1+1+1+..+1+2 selfridges... Whatever you do with 1+1+1+..+1+2 selfridges there will always be counterexamples if you allow a free parameter. I am not saying there will not exist counterexamples for 1+1+1..+1+2+2 -- they are...
 Forum: Miscellaneous Math 2021-04-09, 00:41 Replies: 35 Views: 687 Posted By paulunderwood Nice try. n==3 mod 4 has no counterexample for... Nice try. n==3 mod 4 has no counterexample for the two selfridges test (2+i)^(n+1)==5 mod (n,i^2+1) for n<2^50.
 Forum: Miscellaneous Math 2021-04-06, 14:35 Replies: 35 Views: 687 Posted By paulunderwood Can you express your algorithm in Pari/GP for us?... Can you express your algorithm in Pari/GP for us? Then it will be easier to understand and easier to test (to destruction). If you are working over the complex numbers then raising the base a+b*i...
 Forum: Miscellaneous Math 2021-04-03, 23:47 Replies: 35 Views: 687 Posted By paulunderwood Please give us a worked example for the prime 97.... Please give us a worked example for the prime 97. :smile:
 Forum: Tales From the Crypt(o) 2021-04-03, 21:55 Replies: 280 Views: 67,777 Posted By paulunderwood Our beloved leader (in the UK) is going to... Our beloved leader (in the UK) is going to propose "Covid Passports", a Chinese-like control of the population surreptitiously under the guise of "using every tool in the toolbox to restore the...
 Forum: Factoring 2021-04-02, 20:31 Replies: 23 Views: 591 Posted By paulunderwood I have been Windows-free for at least 20 years. I... I have been Windows-free for at least 20 years. I started out on a ZX81; at Uni used PRIMOS and a DEC VAX system. For my sins I had to use DOS and completed rejected Windows during the 90's when it...
 Forum: Factoring 2021-04-01, 19:45 Replies: 23 Views: 591 Posted By paulunderwood All Linux here. You'll find Linux easier to... All Linux here. You'll find Linux easier to configure to best suit your needs, Be free!
 Forum: GPU Computing 2021-03-22, 14:10 Replies: 3 Views: 367 Posted By paulunderwood Apart from Ubuntu, Fedora is a better choice than... Apart from Ubuntu, Fedora is a better choice than Centos,
 Forum: Miscellaneous Math 2021-03-18, 21:53 Replies: 118 Views: 24,173 Posted By paulunderwood odd r Let a=2^r, r odd and minimal such that kronecker(a^2-1,n)==-1 Test1. Mod(a^2-1.n)^((n-1)/2)==-1 Test2. Mod(Mod(2*x,n),x^2-2*a*a+1)^((n+1)/2)==2*kronecker(a+1) Interestingly counterexamples...
 Forum: Miscellaneous Math 2021-03-18, 19:41 Replies: 118 Views: 24,173 Posted By paulunderwood If n = 2^s+-3, letting b = 5 would mean 2^s-2... If n = 2^s+-3, letting b = 5 would mean 2^s-2 would okay for a base or 2^s -8 would also be okay for a base, since neither are powers ; of 2. So apart from these corner cases taking b=3 should be...
 Forum: Miscellaneous Math 2021-03-18, 06:24 Replies: 118 Views: 24,173 Posted By paulunderwood Getting back on track for this thread... ... Getting back on track for this thread... Let b != +-2^s Let a = b^r where kronecker(a^2-1,n) == -1 Test1: (a^2-1,n)^((n-1)/2) == -1 (mod n) Test2: (b*x)^((n+1)/2) ==...
 Forum: Miscellaneous Math 2021-03-17, 11:07 Replies: 58 Views: 1,407 Posted By paulunderwood http://www.numbertheory.org/ntw/N6.html ... http://www.numbertheory.org/ntw/N6.html http://www.numbertheory.org/ntw/N7.html Why do you not attach it here at MeresenneForum first? At least we can advise you on spelling and typographic...
 Forum: Software 2021-03-15, 22:20 Replies: 13 Views: 407 Posted By paulunderwood Hmm, two workers would do it. Then try four and... Hmm, two workers would do it. Then try four and compare throughput. I think mprime and the Linux scheduler are smart enough to set the right affinities.
 Forum: Software 2021-03-15, 20:53 Replies: 13 Views: 407 Posted By paulunderwood Try 2 instances of 26 cores each, one for each... Try 2 instances of 26 cores each, one for each CPU. And then try 4 instances of 13 cores each and compare throughputs.
 Forum: GPU Computing 2021-03-15, 20:39 Replies: 365 Views: 63,338 Posted By paulunderwood You should be able to afford it if you find the... You should be able to afford it if you find the next Mersenne prime :wink:
 2021-03-15, 16:58 Replies: 48 Sticky: Primo reservation thread Views: 17,000 Posted By paulunderwood Reserving: M86137 cofactor prp25896 M86371... Reserving: M86137 cofactor prp25896 M86371 cofactor prp25984 M87691 cofactor prp26371 E(11848)/(5*1582043) prp40792
 Forum: Miscellaneous Math 2021-03-14, 14:25 Replies: 118 Views: 24,173 Posted By paulunderwood No, it was not the question at the beginning of... No, it was not the question at the beginning of the topic. With only 51 known Mersenne prime < ~25 million digits and your condition being neccesary, we will probably never know of a contradiction...
 Forum: Miscellaneous Math 2021-03-14, 11:33 Replies: 118 Views: 24,173 Posted By paulunderwood Have you noticed that for prime Mp then... Have you noticed that for prime Mp then 3^((Mp-1)/p)==2^r mod Mp for some r? Here 3 is not special. It works for all bases. Anyway this thread was about working (mod n, f) where f is a quadratic...
 2021-03-11, 19:31 Replies: 27 Views: 839 Posted By paulunderwood 3 is special because kronecker(3,Mp)==-1 for all... 3 is special because kronecker(3,Mp)==-1 for all odd p. Lehmer's test (https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test) is an efficient implementation of...
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