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 Showing results 1 to 25 of 311 Search took 0.06 seconds. Search: Posts Made By: carpetpool
 Forum: Miscellaneous Math 2020-09-20, 00:04 Replies: 102 Views: 8,343 Posted By carpetpool The pseudoprimes associated with r=1 are just... The pseudoprimes associated with r=1 are just those 2-SPRPs congruent to 3 mod 4. We need some way to avoid trivial cases. As you suggest, gcd(2^r-2,n)=1 is a good requirement. Whether my claim could...
 Forum: Miscellaneous Math 2020-09-19, 08:35 Replies: 102 Views: 8,343 Posted By carpetpool I retract my original claim (but perhaps... I retract my original claim (but perhaps something better could be turned out of it). Here are some counterexamples I just found using specific parameters b = 2, r = 1, s = 2. Trivially,...
 Forum: Miscellaneous Math 2020-09-17, 15:57 Replies: 54 Views: 1,614 Posted By carpetpool We need an easy computational method to compute... We need an easy computational method to compute b(u) (if deg(b(u)) = p, then forget it, it's practically impossible to compute ). Anyone?
 Forum: Miscellaneous Math 2020-09-17, 15:28 Replies: 102 Views: 8,343 Posted By carpetpool I think the 1-2^r test is better (a... I think the 1-2^r test is better (a generalization to any arbitrary base b should hold). If there are two integers r, s, which pass this test, in particular we have (WLOG): 1 - b^r...
 Forum: Miscellaneous Math 2020-09-17, 03:33 Replies: 54 Views: 1,614 Posted By carpetpool I agree with CRGreathouse. Seems like a... I agree with CRGreathouse. Seems like a pseudoprime (PRP) test. The test can be generalized to higher level matrices. With 2 x 2 matrix test: For any integer n, if we have (gp): ...
 Forum: Prime Wiki 2020-09-14, 04:19 Replies: 210 Sticky: Prime-Wiki Views: 17,449 Posted By carpetpool Williams Primes base 3 I created a page for 10*3^n+1 (https://www.rieselprime.de/ziki/Gen._Proth_prime_3_10) so that Williams PP9 (https://www.rieselprime.de/ziki/Williams_prime_PP_9) primes could be reused from there. ...
 Forum: Lounge 2020-09-10, 17:27 Replies: 1,494 Views: 97,880 Posted By carpetpool I'm really shook to see one of our own members on... I'm really shook to see one of our own members on this forum pass away... :sad: Everyone here is valuable even if we don't all know eachother. RIP Ian
 Forum: Conjectures 'R Us 2020-09-02, 19:22 Replies: 839 Views: 67,492 Posted By carpetpool Yes, I plan to. There are 553 of them now, I'm... Yes, I plan to. There are 553 of them now, I'm hoping to go as far as eliminating at least half of those.
 Forum: Conjectures 'R Us 2020-09-02, 17:33 Replies: 839 Views: 67,492 Posted By carpetpool Would like to please reserve S223. Not sure what... Would like to please reserve S223. Not sure what range I want to complete yet. Will post .res files here since there are a lot of candidates to check.
 Forum: Miscellaneous Math 2020-09-01, 03:16 Replies: 2 Views: 285 Posted By carpetpool Claim: If 2^n-1 is not prime, then 2^(n-2)-1 is a... Claim: If 2^n-1 is not prime, then 2^(n-2)-1 is a quadratic non-residue mod 2^n-1. The claim is false, however the contrapositive is true: If 2^n-1 is prime, then 2^(n-2)-1 is a quadratic...
 Forum: Miscellaneous Math 2020-08-31, 23:01 Replies: 10 Views: 730 Posted By carpetpool The thread discussion raises an interesting... The thread discussion raises an interesting problem I had in mind: For primes q and (odd) p How does one find solutions to x^q = a mod p given that p = 1 mod q^2 provided the solutions exist...
 Forum: carpetpool 2020-08-14, 04:08 Replies: 0 Views: 379 Posted By carpetpool Eliptic curve J-variants I am interesting in understanding the theoretical aspect of the ECPP test, and how everything works. Looking at this...
 Forum: Wagstaff PRP Search 2020-07-26, 13:08 Replies: 0 Views: 219 Posted By carpetpool Wagstaff factors Wagstaff factors currently aren't on the Top20's page and was thinking about asking Prof. Caldwell or one of his editors to consider making an archivable form (https://primes.utm.edu/top20/home.php)...
 Forum: Lounge 2020-07-17, 17:05 Replies: 56 Views: 4,613 Posted By carpetpool Not 25 yet, nor have I been involved in romantic... Not 25 yet, nor have I been involved in romantic relationships just yet. Being a mostly math/computer science/tech forum (myself included), I figured I might ask to those of you who have: How...
 Forum: Riesel Prime Search 2020-07-13, 22:48 Replies: 212 Views: 25,844 Posted By carpetpool Another lucky hit: 26*3^1700041+1 may be... Another lucky hit: 26*3^1700041+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 938.494 sec. 26*3^1700041+1 is prime! (811128 decimal digits) Time : 946.942 sec.
 Forum: sweety439 2020-07-12, 18:55 Replies: 997 Views: 32,058 Posted By carpetpool That is incorrect. What if we only know 12.5% of... That is incorrect. What if we only know 12.5% of the factorization of n^2-1 (CHG proof), and thus, niether n+1, nor n-1 has to be trivially written as a product ? What if the factors found were...
 Forum: Riesel Prime Search 2020-07-12, 05:22 Replies: 1,952 Views: 169,853 Posted By carpetpool 273*2^2024810-1 is prime! (609531 decimal digits)... 273*2^2024810-1 is prime! (609531 decimal digits) Time : 1198.071 sec.
 Forum: Miscellaneous Math 2020-07-08, 19:21 Replies: 14 Views: 762 Posted By carpetpool Cunningham Chain of the second kind... Cunningham Chain of the second kind (https://primes.utm.edu/glossary/page.php?sort=CunninghamChain) OP is mentioning a special case of this (k=2, Fermat Primes), there are only finitely such...
 Forum: Riesel Prime Search 2020-07-06, 03:34 Replies: 212 Views: 25,844 Posted By carpetpool This has been my lucky weekend (just yesterday, I... This has been my lucky weekend (just yesterday, I found a T5K prime for CRUS): 26*3^1435875+1 may be prime, but N divides 3^((N-1)/3))-1, restarting with a=5 Time : 1308.400 sec. 26*3^1435875+1...
 Forum: Conjectures 'R Us 2020-07-04, 20:46 Replies: 864 Sticky: Report top-5000 primes here Views: 66,387 Posted By carpetpool R187 has 4 k's to go now: 2868*187^212559-1... R187 has 4 k's to go now: 2868*187^212559-1 is prime! (482904 decimal digits, P = 3) Time : 5885.318 sec.
 Forum: sweety439 2020-07-03, 17:22 Replies: 20 Views: 2,297 Posted By carpetpool I also did a test with PFGW to verify weather... I also did a test with PFGW to verify weather this number was a 3-PRP, or even 3-SPRP or not: >pfgw64 -q"29*32^1745576-1" PFGW Version 4.0.0.64BIT.20190528.Win_Dev [GWNUM 29.8] ...
 2020-06-30, 19:28 Replies: 9 Views: 843 Posted By carpetpool There appear to be two types of Higher order... There appear to be two types of Higher order Carmichael numbers of order m: n such that p^m-1 | n^m-1 for each prime p | n n such that Phi(d,p) | Phi(d,n) for each prime p | n and each divisor...
 Forum: Miscellaneous Math 2020-06-28, 18:28 Replies: 9 Views: 974 Posted By carpetpool A quick improvement to the test: For n = 3... A quick improvement to the test: For n = 3 mod 4, we have: 1) Find b = t^2 + 1 such that Jacobi(b, n)==1 2) gcd(t^3 - t, n)==1 3) Compute u*x + v = (x + t)^((n + 1)/2) mod (n, x^2 + 1) 4)...
 Forum: Information & Answers 2020-06-22, 05:52 Replies: 18 Views: 1,509 Posted By carpetpool Apart from what others have said, there's nothing... Apart from what others have said, there's nothing stopping you from creating your own algorithm, especially for multiplication. You will want to look at running times of existing algorithms such as...
 Forum: Riesel Prime Search 2020-06-17, 00:56 Replies: 379 Views: 37,558 Posted By carpetpool True. Or until the rate at which candidates are... True. Or until the rate at which candidates are being removed is less than a single LLR test.
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