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 Showing results 1 to 25 of 1000 Search took 0.28 seconds. Search: Posts Made By: paulunderwood
 2021-09-25, 18:36 Replies: 20 Views: 7,300 Posted By paulunderwood :shock: :shock: :shock: :shock: Should that... :shock: :shock: :shock: :shock: Should that not be n=-1..2? And... a=5606879602425*2^1290000-1 and d=33*2^2939063-5606879602425*2^1290000 So a-d is negative :ermm: a+d = 33*2^2939063 - 1
 Forum: Lounge 2021-09-24, 10:26 Replies: 20 Views: 352 Posted By paulunderwood Cost of electricity -- compute for heat only Here in the UK our electricity prices are about to go up by some 66% to in excess of £0,25 per kilowatt hour (plus £0.25 a day for the standing charge). This is a huge increase and is forcing me to...
 2021-09-24, 00:50 Replies: 20 Views: 7,300 Posted By paulunderwood :bow: This is huge! Surely it will top the second... :bow: This is huge! Surely it will top the second table for top20 APs (https://primes.utm.edu/top20/page.php?id=14), with almost unassailable points. Nice ingenuity!
 2021-09-21, 19:46 Replies: 13 Views: 360 Posted By paulunderwood Mod 11 is used to get the check digit of ISBNs... Mod 11 is used to get the check digit of ISBNs https://en.wikipedia.org/wiki/International_Standard_Book_Number#Check_digits
 Forum: Lounge 2021-09-21, 02:02 Replies: 12 Views: 246 Posted By paulunderwood You have a few options for heavy duty prime... You have a few options for heavy duty prime number crunching. Number 1 is GIMPS, maybe you feel lucky and could find the next largest prime. Number 2 is PrimeGrid. They have plenty of sub-projects...
 Forum: Lounge 2021-09-21, 01:37 Replies: 12 Views: 246 Posted By paulunderwood The GPUs have 16GB each, enough to do two sets of... The GPUs have 16GB each, enough to do two sets of P-1 factoring. So 16GB would be more than enough for the mainboaord. However on a more cores board it would be nice to have 64GB. But I reiterate...
 Forum: Lounge 2021-09-21, 01:16 Replies: 12 Views: 246 Posted By paulunderwood Get a water cooled 32 core AMD with a couple of... Get a water cooled 32 core AMD with a couple of secondhand AMD Radeon VII GPUs. Alternatively buy a cheaper computer with sufficient RAM and 4 Radeon VIIs. (I see the secondhand market for R7's on...
 Forum: Riesel Prime Search 2021-09-21, 00:39 Replies: 273 Views: 47,284 Posted By paulunderwood The prof has been busy. He fixed the palindrome... The prof has been busy. He fixed the palindrome length and puzzle-peter's arithmetic progression, which comes second on table two of https://primes.utm.edu/top20/page.php?id=14. Hint: An AP9...
 Forum: Miscellaneous Math 2021-09-19, 13:13 Replies: 7 Views: 178 Posted By paulunderwood Different tack Let the matrix A=[a,-1;1,0] with kronecker(a^2-4,n)==-1 && gcd(a^3-a,n)==1. The latest test (LT) is A^n+t^n == (A+t)^n mod n. with the following GCDs:- gcd(t^3-t,n)==1 gcd(a+t,n)==1...
 Forum: Miscellaneous Math 2021-09-19, 11:19 Replies: 7 Views: 178 Posted By paulunderwood [n, t, t2]=[415681338623, 2106331569, 9028142873]... [n, t, t2]=[415681338623, 2106331569, 9028142873] is a counterexample to the complex test (CT above). Hmm. I will try to find one for which gcd(a^3-a,n)==1. :grin: Well that did not take long to...
 Forum: Miscellaneous Math 2021-09-19, 06:18 Replies: 7 Views: 178 Posted By paulunderwood [n, a, t, t2]=[8473, 2043, 140, 1252] gives a... [n, a, t, t2]=[8473, 2043, 140, 1252] gives a counterexample, but fear not, I have added gcd(a+t,n)==1 (to GT()) to stop degeneration of the determinant t*(t+a)+1 into unity, and gcd(t*a+1,n)==1 for...
 Forum: Miscellaneous Math 2021-09-19, 01:05 Replies: 7 Views: 178 Posted By paulunderwood For the 1+2+2 Selfridges tst_2_4(n,a) it will be... For the 1+2+2 Selfridges tst_2_4(n,a) it will be nice to write some GMP code against Feitsma's list of Fermat 2-PRPs n < 2^64 -- I will have to see how far I can get. :smile:
 Forum: Miscellaneous Math 2021-09-19, 00:07 Replies: 7 Views: 178 Posted By paulunderwood If t = 2 and t2 = 3 then the above general test... If t = 2 and t2 = 3 then the above general test is: { tst_2_3(n,a)= kronecker(a^2-4,n)==-1&& gcd(210,n)==1&& gcd(a+4,n)==1&& gcd(a+6,n)==1&& Mod(2,n)^(n-1)==1&&
 2021-09-18, 20:02 Replies: 80 Sticky: Primo reservation thread Views: 24,803 Posted By paulunderwood Congrats to Facq, Asuncion and Allombert for... Congrats to Facq, Asuncion and Allombert for breaking the ECPP 30k barrier with the proof of U(148091) (https://primes.utm.edu/primes/page.php?id=132721) -- Fibonacci Number with 30,949 decimal...
 Forum: Miscellaneous Math 2021-09-18, 14:54 Replies: 7 Views: 178 Posted By paulunderwood With the counterexample [n, a, t, t2,... With the counterexample [n, a, t, t2, gcd((t*t2)^2-1,n), gcd(t^2-t2^2,n)] = [5983, 5514, 5512, 5982, 1, 1] it is advisable to take the above GCD giving a non-degenerative Fermat PRP-t test. For this...
 Forum: Miscellaneous Math 2021-09-18, 08:37 Replies: 7 Views: 178 Posted By paulunderwood [Side note: gcd(t^3-t,n)==1 might not be required... [Side note: gcd(t^3-t,n)==1 might not be required in the above tests.] I'll try to convey my thinking here. Let A be the matrix [a,-1;1,0] and its characteristic function be X(A). Note that...
 Forum: Miscellaneous Math 2021-09-18, 04:44 Replies: 7 Views: 178 Posted By paulunderwood Singleton / Complex / General Tests -- Trinomiality Preservation Singleton Case - 2 Selfridges If n = 3 mod 4 then (x+2)^(n+1)==5 (mod n, x^2+1), which has been verified to 2^50. Complex Case - Double Test - Two Parameters Only for n==3 mod 4. Let CT(t,n) =...
 Forum: Riesel Prime Search 2021-09-15, 11:19 Replies: 273 Views: 47,284 Posted By paulunderwood No they are not :no: Reversing the digits does... No they are not :no: Reversing the digits does not give the same number. https://primes.utm.edu/primes/page.php?id=132715 is a palindrome. Congrats Serge and Ryan. UTM's Prime Pages parser...
 Forum: Software 2021-09-15, 10:53 Replies: 10 Views: 554 Posted By paulunderwood I don't know about efforts to put GWNUM in GMP,... I don't know about efforts to put GWNUM in GMP, but you could write your own functions like gw_mul( mpz_t r, mpz_t a, mpz_t b ) { ... } :smile:
 Forum: Riesel Prime Search 2021-09-14, 21:01 Replies: 273 Views: 47,284 Posted By paulunderwood I am looking forward to its revelation. The... I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular...
 Forum: Riesel Prime Search 2021-09-12, 17:20 Replies: 273 Views: 47,284 Posted By paulunderwood Congrats to Marc Wiseler and PrimeGrid for the... Congrats to Marc Wiseler and PrimeGrid for the "321" prime 3*2^17748034-1 (https://primes.utm.edu/primes/page.php?id=132678) (5,342,692 decimal digits) ranked as the 18th largest known prime. ...
 Forum: XYYXF Project 2021-09-11, 12:43 Replies: 477 Views: 100,219 Posted By paulunderwood Although it good to us another library, for... Although it good to us another library, for numbers of this size you can use the -tc switch of PFGW to get a combined Fermat+Lucas result, which is much quicker. Congrats for such a huge find.
 Forum: Riesel Prime Search 2021-09-11, 08:21 Replies: 273 Views: 47,284 Posted By paulunderwood Congrats to Serge and Ryan for the two smallest... Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1 10^999999 - 1022306*10^287000 - 1 (https://primes.utm.edu/primes/page.php?id=132705) ...
 Forum: Software 2021-09-09, 11:39 Replies: 7 Views: 322 Posted By paulunderwood That syntax would clash with: You... That syntax would clash with: You could always write a GMP program to do this, or even PARI/GP
 Forum: Information & Answers 2021-09-09, 11:31 Replies: 3 Views: 183 Posted By paulunderwood The 64 core TR comprises of 8 chiplets and so it... The 64 core TR comprises of 8 chiplets and so it is best to run 8 workers at the current wavefront of GIMPS. Forget using Hyper Threading -- only real cores count.
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