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 Showing results 1 to 25 of 1000 Search took 0.40 seconds. Search: Posts Made By: paulunderwood
 2020-09-25, 12:49 Replies: 17 Views: 4,275 Posted By paulunderwood :banana: Congrats for the proof of the M84211... :banana: Congrats for the proof of the M84211 cofactor.
 Forum: Programming 2020-09-24, 00:30 Replies: 15 Views: 2,287 Posted By paulunderwood I don't think GMP switch to special k*b^n+-c like... I don't think GMP switch to special k*b^n+-c like PFGW's implementation of GWNUM. Also PFGW uses GMP below a certain threshold. If GMP has improved PRP times then maybe the author, "rogue",...
 Forum: Lounge 2020-09-24, 00:14 Replies: 12 Views: 526 Posted By paulunderwood LLR or PRP? Ben trial divides to the square root,... LLR or PRP? Ben trial divides to the square root, because he can!
 Forum: Miscellaneous Math 2020-09-23, 23:41 Replies: 102 Views: 8,381 Posted By paulunderwood It is ad hoc. b=3 and all powers of 3 give... It is ad hoc. b=3 and all powers of 3 give counterexamples. I have not found any for b=5 -- I can't recall b=7 counterexample. By plugging in primes to the aforementioned program will show you...
 Forum: Miscellaneous Math 2020-09-23, 23:16 Replies: 102 Views: 8,381 Posted By paulunderwood b=2, b=4 and b=8 seems to give counterexamples 7... b=2, b=4 and b=8 seems to give counterexamples 7 mod 8, as you can see by running the Pari/GP program given in that post.
 Forum: Miscellaneous Math 2020-09-23, 22:50 Replies: 102 Views: 8,381 Posted By paulunderwood Paper + Program Here is a "flawless" replacement paper to a previous paper (https://mersenneforum.org/showthread.php?t=24051&page=8). :book: I have also attached the GMP program used to log cases where GCDs were...
 Forum: Miscellaneous Math 2020-09-23, 22:20 Replies: 102 Views: 8,381 Posted By paulunderwood This thread is supposed to be about PRP tests... This thread is supposed to be about PRP tests using bases over restricted domains, as the content (up until now) shows. It is not really about base changes or coloured balls! Please keep your tripe...
 Forum: Miscellaneous Math 2020-09-22, 17:02 Replies: 102 Views: 8,381 Posted By paulunderwood I can tighten things up by doing the following... I can tighten things up by doing the following test (for any a=2^r): gcd(a-2,n)==1 gcd(a-4,n)==1 kronecker(1-a,n)==-1 Mod(1-a,n)^((n-1)/2)==-1 Mod(2,n)^((n-1)/2)==kronecker(2,n) ...
 Forum: GPU Computing 2020-09-22, 10:02 Replies: 10 Views: 365 Posted By paulunderwood Here are parts of my /etc/default/grub ... Here are parts of my /etc/default/grub GRUB_CMDLINE_LINUX_DEFAULT="quiet amdgpu.ppfeaturemask=0xffffffff" and /boot/grub/grub.cfg linux /boot/vmlinuz-4.19.0-10-amd64...
 Forum: GPU Computing 2020-09-22, 07:24 Replies: 10 Views: 365 Posted By paulunderwood I ran apt-get update (Debian) and the system... I ran apt-get update (Debian) and the system froze while installing ROCm-3.8.0 with the message "building initial module for 4.19-0-9-amd64". Rebooted. I had to do dpkg --configure -a (??) and it...
 Forum: GPU Computing 2020-09-22, 04:50 Replies: 10 Views: 365 Posted By paulunderwood Are you using Linux or Windows? Has the OS... Are you using Linux or Windows? Has the OS upgraded recently?
 Forum: Miscellaneous Math 2020-09-19, 17:44 Replies: 102 Views: 8,381 Posted By paulunderwood A variation on the theme I have been considering x^2-2*x+2^r=0 and have been taking n+1 powers of x over it. I can also take n+1 powers over x^2-(4/2^r-2)+1 and expect the answer to be 1. This gives rise to (yet) another...
 Forum: Miscellaneous Math 2020-09-19, 09:04 Replies: 102 Views: 8,381 Posted By paulunderwood Letting r=1 is trivial as the Euler part becomes... Letting r=1 is trivial as the Euler part becomes Mod(-1)^((n-1)/2). Also it is specified gcd(2-2^r,n)==1 because of x^2-(2^2/2^r-2)*x+1 r=2 does not pass gcd(4-2^r,n)==1. This comes from...
 Forum: GpuOwl 2020-09-18, 09:56 Replies: 56 Views: 4,735 Posted By paulunderwood I think you should have decreased it. I think you should have decreased it.
 Forum: Miscellaneous Math 2020-09-17, 16:41 Replies: 102 Views: 8,381 Posted By paulunderwood Your idea seems right. I ran some of this: {... Your idea seems right. I ran some of this: { forstep(n=30169231,30169231,2, if(!ispseudoprime(n)&&!issquare(n), for(b=1,n,if(gcd(b,n)==1,z=znorder(Mod(b,n)); for(r=1,z,A=Mod(b,n)^r;...
 Forum: GpuOwl 2020-09-17, 05:24 Replies: 2,496 Views: 147,847 Posted By paulunderwood I can't help. I have never used colab. I can't help. I have never used colab.
 Forum: GpuOwl 2020-09-17, 05:18 Replies: 2,496 Views: 147,847 Posted By paulunderwood This is not a bash terminal. Are you using... This is not a bash terminal. Are you using "colab"?
 Forum: GpuOwl 2020-09-17, 05:05 Replies: 2,496 Views: 147,847 Posted By paulunderwood No no. At the terminal enter g++ --version ... No no. At the terminal enter g++ --version Also try g++ followed by hitting tab a couple of times.
 Forum: GpuOwl 2020-09-17, 04:43 Replies: 2,496 Views: 147,847 Posted By paulunderwood What does g++ --version say? You might have... What does g++ --version say? You might have to hardwire your compiler name and version in gpuOwl's makefile.
 Forum: Miscellaneous Math 2020-09-16, 13:42 Replies: 54 Views: 1,626 Posted By paulunderwood Once again it is meaningless to talk about... Once again it is meaningless to talk about "u>log(p)^2" when working with modular arithmetic. Also it makes absolutely no difference where you apply modulo operations. It is a "multiplicative...
 Forum: Miscellaneous Math 2020-09-15, 18:52 Replies: 102 Views: 8,381 Posted By paulunderwood Efficiencies Using Euler+Frobenius on x=1+-sqrt(1-b^4). For intermediate values s*x+t in left-right exponentiation of the Frobenius test we have:- Squaring: ? Mod(s*x+t,x^2-2*x+b^4)^2 Mod((2*s^2 + 2*t*s)*x +...
 Forum: Miscellaneous Math 2020-09-15, 15:50 Replies: 12 Views: 319 Posted By paulunderwood Mod(10,107)^10000000000000000000000000000000000000... Mod(10,107)^100000000000000000000000000000000000000000 Mod(34, 107) ## *** last result computed in 0 ms. It actually works by left-right binary exponentiation modulo n...
 Forum: Miscellaneous Math 2020-09-15, 15:21 Replies: 12 Views: 319 Posted By paulunderwood This Robert at his computer: :primenet: ... This Robert at his computer: :primenet: Know that a*b mod n is the same as (a mod n) * (b mod n) :smile:
 Forum: Miscellaneous Math 2020-09-15, 14:06 Replies: 102 Views: 8,381 Posted By paulunderwood I made a mistake: Case 4 of FLT... I made a mistake: Case 4 of FLT (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Proofs_for_specific_exponents) uses the fact a^4-b^4 is never a square. So I have to flip the sign to get: ...
 Forum: Miscellaneous Math 2020-09-15, 10:44 Replies: 102 Views: 8,381 Posted By paulunderwood test based on FLT proof n=4 In the previous I had x=1+-sqrt(1-2^r). I note that 2^r-1 (r>1) is never a square. So what else is never a square? In his proof of FLT case n=4 Fermat showed a^4+b^4 is never a square, which leads me...
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