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Forum: Abstract Algebra & Algebraic Number Theory 2020-11-30, 00:44
Replies: 2
Views: 61
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...
Forum: Five or Bust - The Dual Sierpinski Problem 2020-11-17, 21:23
Replies: 8
Views: 378
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: 546
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: 862
Views: 76,417
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: 43,867
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: 461
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: 461
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: 450
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: 12,587
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: 12,587
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: 3,698
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: 12,587
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: 3,698
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: 24,448
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: 1,553
RIP
Views: 112,062
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: 862
Views: 76,417
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: 862
Views: 76,417
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: 574
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: 1,324
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: 1,338
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: 601
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: 5,634
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: 29,984
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: 1,112
Views: 42,294
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: 180,039
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.
Showing results 1 to 25 of 319

 
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