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Forum: Five or Bust - The Dual Sierpinski Problem 2020-11-17, 21:23
Replies: 7
Views: 279
Posted By carpetpool
Post 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: 530
Posted By carpetpool
Post 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: 861
Views: 75,422
Posted By carpetpool
Post S223 is complete to n=30k. Primes attached.

S223 is complete to n=30k. Primes attached.
Forum: FermatSearch 2020-10-05, 04:27
Replies: 318
Views: 43,460
Posted By carpetpool
Post 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: 6
Views: 433
Posted By carpetpool
Post 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: 6
Views: 433
Posted By carpetpool
Post 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: 422
Posted By carpetpool
Post 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: 106
Views: 12,230
Posted By carpetpool
Post 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: 106
Views: 12,230
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: 56
Views: 3,556
Posted By carpetpool
Post 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: 106
Views: 12,230
Posted By carpetpool
Post 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: 56
Views: 3,556
Posted By carpetpool
Post 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: 228
Sticky: Prime-Wiki
Views: 23,784
Posted By carpetpool
Post 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: 1,542
RIP
Views: 110,673
Posted By carpetpool
Post 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: 861
Views: 75,422
Posted By carpetpool
Post 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: 861
Views: 75,422
Posted By carpetpool
Post 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: 555
Posted By carpetpool
Post 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: 1,253
Posted By carpetpool
Post 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: 1,257
Posted By carpetpool
Post 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: 580
Posted By carpetpool
Post 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: 5,569
Posted By carpetpool
Post 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: 214
Views: 29,534
Posted By carpetpool
Post 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: 1,111
Views: 41,596
Posted By carpetpool
Post 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: 1,955
Views: 179,303
Posted By carpetpool
Post 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: 1,366
Posted By carpetpool
Post 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...
Showing results 1 to 25 of 318

 
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