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 Showing results 1 to 25 of 1000 Search took 0.27 seconds. Search: Posts Made By: paulunderwood
 2021-04-21, 15:28 Replies: 22 Views: 674 Posted By paulunderwood I am currently testing it for Lucas over x^2-4*x+1 I am currently testing it for Lucas over x^2-4*x+1
 Forum: Riesel Prime Search 2021-04-20, 22:08 Replies: 243 Views: 41,056 Posted By paulunderwood The rep-digit is an admirable find. The rep-digit is an admirable find.
 2021-04-20, 22:07 Replies: 22 Views: 674 Posted By paulunderwood That is one hell of a PRP. Congrats on such a... That is one hell of a PRP. Congrats on such a large find. :smile:
 Forum: Factoring 2021-04-20, 17:42 Replies: 32 Views: 856 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: 549 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: 188 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: 188 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: 188 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: 13 Views: 302 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: 690 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: 690 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: 690 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: 690 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: 68,191 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: 32 Views: 856 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: 32 Views: 856 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: 375 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: 24,240 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: 24,240 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: 24,240 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: 1,411 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: 412 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: 412 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: 63,741 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: 17,084 Posted By paulunderwood Reserving: M86137 cofactor prp25896 M86371... Reserving: M86137 cofactor prp25896 M86371 cofactor prp25984 M87691 cofactor prp26371 E(11848)/(5*1582043) prp40792
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