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 Showing results 1 to 25 of 1000 Search took 0.27 seconds. Search: Posts Made By: paulunderwood
 Forum: Hardware 2021-06-22, 05:12 Replies: 197 Views: 26,731 Posted By paulunderwood I can only think you program this as: ... I can only think you program this as: numactl -m 1 stage1; numactl -m 0 stage2
 Forum: Miscellaneous Math 2021-06-21, 23:34 Replies: 16 Views: 1,259 Posted By paulunderwood Only x^2-2^r*x-4 Based on only x^2-2^r*x-4 ... And it's clunky: { tst(n,r)=local(t=lift(Mod(2,n)^r)); ((n%4==1&&gcd(t^2+4,n)==1)|| (n%4==3&&gcd(t^2+8,n)==1))&& kronecker(t^2+16,n)==-1&&
 Forum: Miscellaneous Math 2021-06-21, 20:49 Replies: 16 Views: 1,259 Posted By paulunderwood base 3 variant This time based on x^2-3^r*x+-9 ... n%4==1: { tst(n,r)=local(t=lift(Mod(3,n)^r)); gcd(t^2-3,n)==1&&gcd(t^2-9,n)==1&& kronecker(t^2-4*9,n)==-1&& Mod(3,n)^(n-1)==1&&
 Forum: Miscellaneous Math 2021-06-21, 16:48 Replies: 16 Views: 1,259 Posted By paulunderwood 1+2 selfridges Based on x^2-2^r*x+-4 ... If n%4==1 then: { tst(n,r)=local(t=lift(Mod(2,n)^r)); gcd(t^2-4,n)==1&& kronecker(t^2-16,n)==-1&& Mod(2,n)^(n-1)==1&&
 Forum: Miscellaneous Math 2021-06-20, 17:33 Replies: 16 Views: 1,259 Posted By paulunderwood I have verified this for all r for all n<10^11. ... I have verified this for all r for all n<10^11. I will convert to GMP soon.
 Forum: Miscellaneous Math 2021-06-20, 05:04 Replies: 16 Views: 1,259 Posted By paulunderwood Efficent Test The efficient test is: { tst(n,r)=local(t=lift(Mod(1/2,n)^r)); gcd(t^2-1,n)==1&& gcd(t-2,n)==1&& kronecker(t^2-4*t,n)==-1&& Mod(2,n)^((n-1)/2)==kronecker(t,n)&&...
 Forum: Miscellaneous Math 2021-06-20, 00:22 Replies: 16 Views: 1,259 Posted By paulunderwood Extra gcd This test looks good: { tst(n,r)=local(t=lift(Mod(2,n)^r)); gcd(t^2-1,n)==1&& gcd(2*t-1,n)==1&& kronecker(1-4*t,n)==-1&& Mod(2,n)^((n-1)/2)==kronecker(t,n)&&...
 Forum: Miscellaneous Math 2021-06-19, 08:02 Replies: 16 Views: 1,259 Posted By paulunderwood Restricted domain variation Here I test over x^2-x+2^r where kronecker(1-4*2^r,n)==-1 x^2-x-2^r where kronecker(1+4*2^r,n)==-1 If r is even this is the same as: 2^(n-1)==1 (mod n) x^((n+1)/2)==1 (mod n,...
 Forum: Hardware 2021-06-13, 23:09 Replies: 197 Views: 26,731 Posted By paulunderwood 1. Check NUMA is on in BIOS whatever that is!... 1. Check NUMA is on in BIOS whatever that is! :smile: 2, Installation: sudo yum install numactl To see the memory map: numactl -H To run yr_prog entirely binded to MCDRAM: numactl -m 1...
 Forum: Hardware 2021-06-13, 22:35 Replies: 197 Views: 26,731 Posted By paulunderwood This is way out of my depth, but do you have a... This is way out of my depth, but do you have a good reason for not using numactl in flat-mode? Have you tried timings using it?
 Forum: sweety439 2021-06-13, 21:21 Replies: 11 Views: 183 Posted By paulunderwood You have Windoze Install on it Sun's free... You have Windoze Install on it Sun's free Virtual Box In Virtual Box install Ubuntu In Ubuntu install the latest multi-core Primo Profit That old mono-processor software will not get you...
 Forum: Hardware 2021-06-13, 03:11 Replies: 197 Views: 26,731 Posted By paulunderwood 1, is bad news. The access to the DIMMs must be... 1, is bad news. The access to the DIMMs must be much slower than the MCDRAM -- an expensive lesson. With them, do you have a great 68-instances P-1 machine? See the table on this page...
 Forum: Miscellaneous Math 2021-06-11, 23:15 Replies: 16 Views: 1,259 Posted By paulunderwood [n,P,Q,R]=[1162349, 2335, 1, 2234] fools tst4(). ... [n,P,Q,R]=[1162349, 2335, 1, 2234] fools tst4(). I have now revised the test; I insist that gcd(Q^2-1,n)==1 and gcd(R^2-1,n)==1 as well. :grin: ...
 Forum: Lounge 2021-06-11, 09:41 Replies: 396 Views: 56,542 Posted By paulunderwood Like a fool I answered my phone. "This is your... Like a fool I answered my phone. "This is your service provider, your router has been hacked and I am here to fix it", said the woman with an Indian accent. Step-by-step instructions to install...
 Forum: Hardware 2021-06-10, 23:09 Replies: 197 Views: 26,731 Posted By paulunderwood I run Debian Buster on my Phi. Forget... I run Debian Buster on my Phi. Forget multithreading on these beasts. 64 instances is king for mine, although I am running 4 Primo instances with its 256 threads. I don't know how Ernst's code copes.
 Forum: Miscellaneous Math 2021-06-10, 20:57 Replies: 16 Views: 1,259 Posted By paulunderwood Well that was a lot of BS maths. I... Well that was a lot of BS maths. I have tested (with strong kroneckers and gcd(P,n)==1 and gcd(Q^2-R^2,n)==1) for Q=1 up to n < 10^6 and for all Q for n up to 1.8*10^4 with Pari/GP. When I get...
 Forum: Miscellaneous Math 2021-06-09, 18:39 Replies: 145 Views: 8,462 Posted By paulunderwood :dnftt: :dnftt:
 Forum: Miscellaneous Math 2021-06-08, 00:13 Replies: 16 Views: 1,259 Posted By paulunderwood What is wrong with this argument? Let: ... What is wrong with this argument? Let: x^2-P*x+Q=0 y^2-P*y-Q=0 s^2-P*s+R=0 t^2-P*t-R=0 Then: x^2+y^2-P*(x+y)=0
 Forum: Miscellaneous Math 2021-06-07, 07:35 Replies: 16 Views: 1,259 Posted By paulunderwood tst4(9809, 577, 27, 171) fails, but if I add the... tst4(9809, 577, 27, 171) fails, but if I add the remedy gcd(P,n)==1 all is good.
 Forum: Miscellaneous Math 2021-06-06, 10:53 Replies: 16 Views: 1,259 Posted By paulunderwood I have not yet found a counterexample to the... I have not yet found a counterexample to the previous test. I now propose a more general test: { tst(n,P,Q_i,Q_j)= kronecker(P^2-4*Q_i)==-1&& kronecker(P^2+4*Q_i)==-1&&...
 2021-06-05, 14:18 Replies: 71 Sticky: Primo reservation thread Views: 21,543 Posted By paulunderwood These are not "top20" special forms at the... These are not "top20" special forms at the PrimePages. They would take you 16 times as long each as the 10k digit primes you certified.
 Forum: Miscellaneous Math 2021-06-02, 07:23 Replies: 10 Views: 363 Posted By paulunderwood More attacks on our hard efforts! "Only 28709... More attacks on our hard efforts! "Only 28709 digits" -- have you tried running Primo, even at 10k digits? it is O(log(n)^(4+eps)). It is not trivial to do such certifications. It is absurd to say...
 Forum: Hardware 2021-06-01, 20:58 Replies: 197 Views: 26,731 Posted By paulunderwood 3*2^6000000-1 with 64 instances (optimal) is 4.15... 3*2^6000000-1 with 64 instances (optimal) is 4.15 ms/iter. About 7 hours per test. (Xeon Phi 7210) YMMV.
 Forum: Operation Billion Digits 2021-05-30, 14:10 Replies: 11 Views: 1,188 Posted By paulunderwood :crank: How do you propose to do PRP/LL... :crank: How do you propose to do PRP/LL tests? What hardware and on it how long do you expect a single test to complete?
 Forum: Miscellaneous Math 2021-05-29, 05:31 Replies: 10 Views: 363 Posted By paulunderwood These numbers take months if not years of... These numbers take months if not years of certification on dedicated hardware. Maybe you could invest some time and money in the endeavors to provide such proofs instead of squawking about how...
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