k=1 thru k=12

[kar_bon]

4*513^38031-1 is prime

[sweety439]

8*728^7399+1 is prime.

[sweety439]

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.

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.

Are there any update of these files? e.g. recently the prime 8*410^279991+1 (for Sierpinski k=8) was found.

[gd_barnes]

The files in post #62 have been updated.

[gd_barnes]

I searched all remaining k<=12 and b<=1030 up to n=25K. There were 45 k/base combos for k=8 thru 12 that needed to be searched for n=5K-25K. I found the following 11 primes:

8*997^15814-1
9*990^23031-1
10*599^11775-1
12*593^16063-1
10*537^7117+1
10*827^9894+1
10*929^13064+1
10*1004^10644+1
12*600^11241+1
12*607^7582+1
12*673^7789+1

The files in post #62 have been updated accordingly.

[sweety439]

Originally Posted by gd_barnes

I searched all remaining k<=12 and b<=1030 up to n=25K. There were 45 k/base combos for k=8 thru 12 that needed to be searched for n=5K-25K. I found the following 11 primes:

8*997^15814-1
9*990^23031-1
10*599^11775-1
12*593^16063-1
10*537^7117+1
10*827^9894+1
10*929^13064+1
10*1004^10644+1
12*600^11241+1
12*607^7582+1
12*673^7789+1

The files in post #62 have been updated accordingly.

So you can add the prime 8*997^15814-1 in the CRUS page, currently R997 is only tested to n=10K.

[kar_bon]

I've included two pages in the Prime-Wiki for these values:

- Riesel type
- Proth type

I took the data from post #62, compiled as CSV (link for download given) for all 2 ≤ k ≤ 12 and displayed all wanted values. The table columns are sortable.

[Dylan14]

I am presently working on trying to find a prime for 7*1004^n+1, currently past 50k, will take to n = 100k.

[Dylan14]

And we have a prime:

7*1004^54848+1 is 3-PRP! (97.6687s+0.0034s)


C:\Users\Dylan\Desktop\prime finding\prime testing\pfgw>pfgw64 -t -q"7*1004^54848+1"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing 7*1004^54848+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
7*1004^54848+1 is prime! (93.6171s+0.0033s)

With this, all bases within CRUS limits (b <= 1030) have a prime for k = 7 on the Sierpinski side. (*)


(*) if they are not excluded by covering sets.

[sweety439]

Originally Posted by Dylan14

And we have a prime:

7*1004^54848+1 is 3-PRP! (97.6687s+0.0034s)


C:\Users\Dylan\Desktop\prime finding\prime testing\pfgw>pfgw64 -t -q"7*1004^54848+1"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing 7*1004^54848+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
7*1004^54848+1 is prime! (93.6171s+0.0033s)

With this, all bases within CRUS limits (b <= 1030) have a prime for k = 7 on the Sierpinski side. (*)


(*) if they are not excluded by covering sets.

Great!!! Now there are no remain bases for Sierp k=7!!! Besides, how about reserving 2*801^n+1, the only form only searched to n=25K for Sierp k=2.

[kar_bon]

Checked 6*299^n-1 from n=25k (up to 65k) and found:

6*299^64897-1 is prime!