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 Showing results 1 to 25 of 333 Search took 0.05 seconds. Search: Posts Made By: carpetpool
 Forum: Miscellaneous Math 2022-07-03, 02:55 Replies: 0 Views: 80 Posted By carpetpool Is it possible for an odd perfect number to have the form 8*k+5? From Euler's Criterion of an odd perfect number n, we know that n = p^m*s^2 for a prime p = 1 mod 4 and exponent m = 1 mod 4. Consequently, n is the sum of two squares. Is n necessarily the...
 Forum: Msieve 2022-01-05, 06:45 Replies: 4 Views: 608 Posted By carpetpool Thanks, your suggestion seemed to work. Also, is... Thanks, your suggestion seemed to work. Also, is the same true for NFS (YAFU better than Msieve), presumably for 130+ digits?
 Forum: Msieve 2022-01-04, 04:54 Replies: 4 Views: 608 Posted By carpetpool Msieve Quadratic Sieve error I am (somewhat) new to using Msieve (and factoring projects too), I am trying to factor this random semiprime as a performance test, and I get the following error: Mon Jan 03 20:08:41 2022 Msieve...
 Forum: Conjectures 'R Us 2022-01-01, 18:59 Replies: 1,039 Sticky: Report top-5000 primes here Views: 140,922 Posted By carpetpool A good start... A good start (https://primes.utm.edu/primes/page.php?id=133119) to a new year. :smile:
 Forum: Factoring 2021-12-28, 21:28 Replies: 4 Views: 979 Posted By carpetpool Significance of 'strong primes'? This is more of a theoretical question, but what is the importance of a 'strong prime', specifically, the second property illustrated on the Wikipedia page here...
 Forum: Miscellaneous Math 2021-11-12, 00:10 Replies: 4 Views: 825 Posted By carpetpool As per that post, I can see the argument made... As per that post, I can see the argument made against my original claim (not that it's incorrect, but rather contradicting). The probability of Mp = 2^p-1 being prime is C/p where C is a...
 Forum: Miscellaneous Math 2021-11-10, 05:09 Replies: 4 Views: 825 Posted By carpetpool Mersenne prime exponents that are also Sophie Germain primes So I stumbled on A065406 (http://oeis.org/A065406) by curiosity, and somewhere in the comments said this list was expected to be finite. Basically, the number of primes p such that 2*p+1 and 2^p-1...
 Forum: carpetpool 2021-11-08, 17:02 Replies: 1 Views: 679 Posted By carpetpool Some T5K prime ideas So most primes on the T5K list as you all might know are primes of the form k*b^n+-1 where k and b are rather small. While I haven't searched for many primes in a long time, I thought of trying...
 Forum: Conjectures 'R Us 2021-10-01, 23:04 Replies: 989 Views: 133,076 Posted By carpetpool Back at it again... Will reserve S157. I... Back at it again... Will reserve S157. I plan to get at least to 400k on it but may go further... it depends.
 Forum: sweety439 2021-01-09, 21:44 Replies: 355 Views: 45,661 Posted By carpetpool Here's a suggestion: Instead of constantly... Here's a suggestion: Instead of constantly posting search limits and reservations that can be done in minutes, use a doc or pdf instead. Attach or provide the link in a single post. If you need...
 Forum: Math 2021-01-08, 03:31 Replies: 26 Views: 6,240 Posted By carpetpool Déjà... Déjà (https://www.mersenneforum.org/showpost.php?p=563216&postcount=3) vu (https://www.mersenneforum.org/showthread.php?p=563218)?
 Forum: carpetpool 2021-01-03, 22:16 Replies: 1 Views: 2,056 Posted By carpetpool The examples involving Trinomial Coefficients and... The examples involving Trinomial Coefficients and Catalan numbers (also see here (https://en.wikipedia.org/wiki/Catalan_pseudoprime)) are examples of P-recursive sequences, which is what I am...
 Forum: carpetpool 2020-12-30, 09:50 Replies: 1 Views: 2,056 Posted By carpetpool Computation of P-Recursive Sequences in Polynomial Time Is it possible for centered trinomial coefficients (https://mathworld.wolfram.com/CentralTrinomialCoefficient.html) to be computed in O(log n) time, analogous to how the time complexity of modular...
 Forum: Riesel Prime Search 2020-12-12, 09:08 Replies: 307 Views: 61,060 Posted By carpetpool Very interesting, indeed. The prime in... Very interesting, indeed. The prime in question does not appear to be totally random? I have actually constructed large random provable primes before (over 100,000 digits), but none of them...
 2020-12-08, 06:31 Replies: 42 Views: 19,562 Posted By carpetpool You can test them with LLR, you will just need to... You can test them with LLR, you will just need to format your candidates to a NewPGEN type header. Here is an example for n*3^n+1: 200000:P:1:3:257 32 32 34 34 54 54 76 76 114 114 128 128...
 2020-12-02, 21:19 Replies: 8 Views: 10,433 Posted By carpetpool Then write up a paper explaining your... Then write up a paper explaining your conjectures, and provide more evidence for your claims, like I have given or some of your own research.
 2020-11-30, 00:44 Replies: 8 Views: 10,433 Posted By carpetpool Finding the expected number of primes of... Finding the expected number of primes of (k*b^n+c)/gcd(k+c,b-1) shouldn't be much different than finding the expected number of primes of the form k*b^n+c. If we treat numbers of the form k*b^n+c as...
 2020-11-17, 21:23 Replies: 8 Views: 11,535 Posted By carpetpool I would happily certify it if I had the... I would happily certify it if I had the resources. Unfortunately for Primo (which can run about 64 concurrent tasks at a time), the time complexity for certifying N prime is at least O(ln(N)^4). I...
 Forum: Miscellaneous Math 2020-11-17, 20:54 Replies: 21 Views: 2,390 Posted By carpetpool There appear to be a handful of pseudoprimes... There appear to be a handful of pseudoprimes without the BPSW requirement: for(n=1,30000, if(n%2==1 & isprime(n)==0, for(a=1,n, if(kronecker(a^2-4,n)==(-1) & kronecker(a^4-8*a^2+12,n)==(-1) &...
 Forum: Conjectures 'R Us 2020-10-12, 05:34 Replies: 989 Views: 133,076 Posted By carpetpool S223 is complete to n=30k. Primes attached. S223 is complete to n=30k. Primes attached.
 Forum: FermatSearch 2020-10-05, 04:27 Replies: 345 Sticky: New Fermat factors Views: 94,332 Posted By carpetpool Congrats on a World Record Fermat Divisor! ... Congrats on a World Record Fermat Divisor! :bounce wave: PrimeGrid has held the record for many years up until now... Way to go!
 Forum: Software 2020-10-04, 22:39 Replies: 24 Views: 3,057 Posted By carpetpool Thanks for the suggestions! I ran 4 subsequent... Thanks for the suggestions! I ran 4 subsequent instances of LLR --- assigning affinity to CPUS 0, 2. The time increased by about 0.120 ms which I guess makes sense given that more cores means...
 Forum: Software 2020-10-03, 21:16 Replies: 24 Views: 3,057 Posted By carpetpool LLR Affinity Problem I know there's a way to run different LLR instances and have them assigned to different designated CPU, making it run significantly faster than if only one instance were used. I am using a 4 core,...
 Forum: GPU Computing 2020-10-02, 21:41 Replies: 1 Views: 2,387 Posted By carpetpool LLR GPU application Hi, I'm wondering if the GPU LLR software found at Jean Penne's website (http://jpenne.free.fr/index2.html) is in progress or of any use. I've installed CUDA Toolkit 11.1...
 Forum: Miscellaneous Math 2020-09-20, 00:04 Replies: 118 Views: 32,649 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...
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