k=1 thru k=12 - Page 7

sweety439 · 2017-02-01, 13:34

Found an additional exclusion:

Riesel k=12: base 307 has a covering set of [5, 11, 29]

Thus, there are only 6 bases remain for Riesel k=12: 263, 593, 615, 717, 912, 978.

sweety439 · 2017-02-01, 15:43

Also, for the "number of remaining k's" column of the text files for the remain bases, why 7*1004^n+1 and 10*1004^n+1 lists 3k, but 2*1004^n+1 lists 1k? As you say, S1004 should list 3k since k=2, 7 and 10 remain for that same base, like the example for S593, all 4*593^n+1, 8*593^n+1 and 12*593^n+1 list 3k since k=4, 8 and 12 remain for that same base, and the example for S824, both 5*824^n+1 and 8*824^n+1 lists 2k since k=5 and 8 remain for that same base, but why for S230, 12*230^n+1 lists 2k but 4*230^n+1 lists 1k? S230 should list 2k since k=4 and 12 remain for that same base.

gd_barnes · 2017-02-01, 22:24

My files have been fixed on my machine. Whenever I post them again, you will see the corrections.

LaurV · 2017-02-09, 01:39

Quote:

Originally Posted by gd_barnes

Great thanks! I keep my files updated with all primes found for these from everyone. I will note that one.

One more, turned out by LLR this morning:

2*522^62288-1 is prime! (169279 decimal digits, P = 29) Time : 768.095 sec.

And out of your interest range, but yet ok for our sweety-tweety (see the thread I posted yesterday about cllr bug),

2*1487^36432-1 is prime! (115574 decimal digits, P = 9) Time : 420.446 sec.

sweety439 · 2017-02-09, 15:49

There is a research for k=2 and some Sierpinski/Riesel bases (including some bases b>1030): http://mersenneforum.org/showthread.php?t=6918

sweety439 · 2017-03-10, 19:10

Quote:

Originally Posted by gd_barnes

I have now searched k=11 and 12 for all bases <= 1030. Therefore all k=2 thru 12 for all bases <= 1030 have been completed. All k=2 thru 7 have been searched to n=25K for all bases and k=8 thru k=12 have been searched to n=5K for all bases.

Attached are all primes for n<=5K found by my effort, n>5K found by CRUS, and bases remaining for each k. There have been some updates for k=2 thru 10 so all of k=2 thru 12 are included.

Below are all exclusions including bases with trivial factors, algebraic factors, and covering sets for k=11 and 12. Exclusions for k<=10 were previously posted.

Code:

Riesel k=11:
b==(1 mod 2) has a factor of 2
b==(1 mod 5) has a factor of 5
b==(14 mod 15) has a covering set of [3, 5]

Riesel k=12:
b==(1 mod 11) has a factor of 11
b==(142 mod 143) has a covering set of [11, 13]
base 307 has a covering set of [5, 11, 29]
base 901 has a covering set of [7, 11, 13, 19]

Sierp k=11:
b==(1 mod 2) has a factor of 2
b==(1 mod 3) has a factor of 3
b==(14 mod 15) has a covering set of [3, 5]

Sierp k=12:
b==(1 mod 13) has a factor of 13
b==(142 mod 143) has a covering set of [11, 13]
bases 562, 828, and 900 have a covering set of [7, 13, 19]
base 563 has a covering set of [5, 7, 13, 19, 29]
base 597 has a covering set of [5, 13, 29]
bases 296 and 901 have a covering set of [7, 11, 13, 19]
base 12 is a GFN with no known prime

I am done with this effort. As the k's get higher, the exclusions get much more complex. Many of the bases for k>=8 are only searched to n=5K. That would be a good starting point for people to do some additional searching if they are interested in this effort.

@Gary, your text file for n > 5K for Riesel k=10 is not right, 10*992^5443-1 is not prime, it is divisible by 7.

MisterBitcoin · 2017-03-10, 19:26

Quote:

Originally Posted by sweety439

@Gary, your text file for n > 5K for Riesel k=10 is not right, 10*992^5443-1 is not prime, it is divisible by 7.

Code:

Primality testing 10*992^5443-1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Factored: 13
composite
10*992^5443-1 is composite (5.8175s+0.0003s)

gd_barnes · 2017-03-10, 21:10

OK thanks. The prime is 10*992^5433-1. There was a typo in my file. I have corrected it on my machine.

gd_barnes · 2017-03-23, 05:31

I have updated the file links in post 62 here with the most recent corrections and updates.

sweety439 · 2017-08-16, 17:58

I am now reserving 2*801^n+1, 7*1004^n+1, 10*449^n+1 and 12*312^n+1 and found that 10*449^18506+1 is prime. (2*801^n+1 is currently at n=26600, 7*1004^n+1 is currently at n=28374, and 12*312^n+1 is currently at n=12394, all no prime found)

This is the result text file for 10*449^n+1.

gd_barnes · 2017-08-16, 22:27

I have updated the files in post #62.

2017-02-01, 13:34	#67
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5·7·83 Posts	Found an additional exclusion: Riesel k=12: base 307 has a covering set of [5, 11, 29] Thus, there are only 6 bases remain for Riesel k=12: 263, 593, 615, 717, 912, 978. Last fiddled with by sweety439 on 2017-02-01 at 13:38

2017-02-01, 15:43	#68
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5·7·83 Posts	Also, for the "number of remaining k's" column of the text files for the remain bases, why 71004^n+1 and 101004^n+1 lists 3k, but 21004^n+1 lists 1k? As you say, S1004 should list 3k since k=2, 7 and 10 remain for that same base, like the example for S593, all 4593^n+1, 8593^n+1 and 12593^n+1 list 3k since k=4, 8 and 12 remain for that same base, and the example for S824, both 5824^n+1 and 8824^n+1 lists 2k since k=5 and 8 remain for that same base, but why for S230, 12230^n+1 lists 2k but 4230^n+1 lists 1k? S230 should list 2k since k=4 and 12 remain for that same base. Last fiddled with by sweety439 on 2017-02-01 at 16:08

2017-02-01, 22:24	#69
gd_barnes May 2007 Kansas; USA 101×103 Posts	My files have been fixed on my machine. Whenever I post them again, you will see the corrections.

2017-02-09, 15:49	#71
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5·7·83 Posts	There is a research for k=2 and some Sierpinski/Riesel bases (including some bases b>1030): http://mersenneforum.org/showthread.php?t=6918

2017-03-10, 21:10	#74
gd_barnes May 2007 Kansas; USA 10403₁₀ Posts	OK thanks. The prime is 10*992^5433-1. There was a typo in my file. I have corrected it on my machine.

2017-03-23, 05:31	#75
gd_barnes May 2007 Kansas; USA 101×103 Posts	I have updated the file links in post 62 here with the most recent corrections and updates.

2017-08-16, 22:27	#77
gd_barnes May 2007 Kansas; USA 101·103 Posts	I have updated the files in post #62.