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Search: Posts Made By: carpetpool
Forum: sweety439 2020-07-12, 18:55
Replies: 900
Views: 25,758
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: 1,949
Views: 166,108
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: 10
Views: 171
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...
Forum: Riesel Prime Search 2020-07-06, 03:34
Replies: 208
Views: 23,062
Posted By carpetpool
Post 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: 848
Views: 61,728
Posted By carpetpool
Post 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: 1,890
Posted By carpetpool
Post 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]
...
Forum: Computer Science & Computational Number Theory 2020-06-30, 19:28
Replies: 9
Views: 396
Posted By carpetpool
Post 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: 643
Posted By carpetpool
Post 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: 670
Posted By carpetpool
Post 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: 361
Views: 32,966
Posted By carpetpool
Post 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.
Forum: Twin Prime Search 2020-06-15, 21:51
Replies: 258
Views: 28,122
Posted By carpetpool
Post Here is the complete set: Bases <= 24 checked to...

Here is the complete set: Bases <= 24 checked to n=5K, others < 100 checked to n=2K. Also verified smaller twin primes, which I had forgot most of them in my previous list.
Forum: Proth Prime Search 2020-06-12, 05:34
Replies: 5
Views: 426
Posted By carpetpool
Post I think you are referring to Gaussian Mersenne...

I think you are referring to Gaussian Mersenne norms (https://primes.utm.edu/top20/page.php?id=41).
Forum: Twin Prime Search 2020-06-11, 20:13
Replies: 258
Views: 28,122
Posted By carpetpool
Post I don't suppose newpgen + pfgw would be faster...

I don't suppose newpgen + pfgw would be faster than twinsieve ?


Here are the twin primes bases up to 48:

k*b^n+-1 with k <= n

base = 3 (check to n=15000)
2*3^2+1
8*3^10+1
Forum: Twin Prime Search 2020-06-09, 22:09
Replies: 258
Views: 28,122
Posted By carpetpool
Post k*b^n+-1 with k < n?

Also another interesting problem if anyone's interested:

Twin primes of the form k*b^n+-1 with k < n -->


Due to the limited choices of fixing only base b, there are extremely rare. I tested...
Forum: sweety439 2020-06-08, 23:23
Replies: 900
Views: 25,758
Posted By carpetpool
Post You could try a simple GP script to eliminate...

You could try a simple GP script to eliminate most k's:

For instance, (k*3^n+1)/2, we have the following k's remaining at n=3000:

h=[]; for(i=1,3000, for(t=1,#g, if(ispseudoprime(...
Forum: sweety439 2020-06-08, 03:10
Replies: 900
Views: 25,758
Posted By carpetpool
Post (k*b^n+c)/gcd(k+c, b-1) is not a polynomial...

(k*b^n+c)/gcd(k+c, b-1) is not a polynomial sequence so it isn't at all related to the Bunyakovsky conjecture. Steps 1 and 2 are trivial enough, but steps 3 and 4 are what make the difference. Step 4...
Forum: And now for something completely different 2020-06-03, 18:00
Replies: 45
Views: 5,789
Posted By carpetpool
Post p = 1 mod 4 increases the odds of such a prime,...

p = 1 mod 4 increases the odds of such a prime, as N = 6*p^n+1 is congruent 7 mod 8, but there is still 1/3 chance --- which at 965K digits, I'm not sure if anyone would be willing to test if N |...
Forum: And now for something completely different 2020-05-30, 19:44
Replies: 45
Views: 5,789
Posted By carpetpool
Post There is also this (https://oeis.org/A332763)...

There is also this (https://oeis.org/A332763) possible sequence I am approaching the T5K range for. It would be interesting to find a prime (k=6) making the "Divides Phi" achievable class...
Forum: And now for something completely different 2020-05-18, 17:10
Replies: 19
Views: 563
Posted By carpetpool
Post How did you sieve them though? I figured you...

How did you sieve them though? I figured you could use the -w option BTW.
Forum: And now for something completely different 2020-05-17, 19:26
Replies: 19
Views: 563
Posted By carpetpool
Post Srsieve is for numbers of the form k*b^n+-c and...

Srsieve is for numbers of the form k*b^n+-c and sr2sieve requires that k=1 or c=1. Thus, you would have to find a program that sieves your requested forms, or use the -f switch in pfgw instead of a...
Forum: And now for something completely different 2020-05-17, 06:55
Replies: 19
Views: 563
Posted By carpetpool
Post I don't know of any utility that does this but...

I don't know of any utility that does this but srfile:

>>> srfile --help
srfile 0.6.17 -- A file utility for srsieve.
Usage: srfile [OPTION ...] <INFILE ...>
-o --output FILE Write...
Forum: Miscellaneous Math 2020-05-15, 18:39
Replies: 16
Views: 491
Posted By carpetpool
Post You seem to have the right idea. You want to...

You seem to have the right idea. You want to calculate 2^n for some integer n. However, this integer n is the one you want to test for primality, and not even 2^n, but 2^n mod n. (n may have,...
Forum: sweety439 2020-05-15, 18:33
Replies: 162
Views: 9,483
Posted By carpetpool
Post Sieving/Reserving MP 11 Ranges will be...

Sieving/Reserving MP 11

Ranges will be updated and posted later.
Forum: And now for something completely different 2020-05-15, 08:06
Replies: 19
Views: 563
Posted By carpetpool
Post You don't want to use -G, or at least it's not...

You don't want to use -G, or at least it's not the simplest way to accomplish what you're asking. The text files are essentially 'prp' files, I combined them into one abcd file:

srfile -a...
Forum: sweety439 2020-05-09, 00:32
Replies: 162
Views: 9,483
Posted By carpetpool
Post I'm working on a posting sieve files for some...

I'm working on a posting sieve files for some sequences so situations like these won't occur again. Anybody can test them as long as they reserve that sequence. I'm expecting to have some sequences...
Showing results 1 to 25 of 296

 
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