Riesel bases 458 and 368
 

Reserving

Reserving Sierp 397 as new to n=25K

Removed 49*476^n-1 from the recommended bases list found prime by Max.

S475 with a CK of 288 is proven with a largest prime of 34*475^1387+1. Details on the pages.

This is the largest CK proof of any Sierp base > 300 to date! :smile:

I will now attempt to match on the Sierp side Max's 5 consecutive Riesel bases 472 to 476 proven. With S473/S474/S475 now proven and S475 having the highest CK in the group of 5, I will reserve S472 and S476 and also S470 for grins; all to n=25K.

R365 is proven

CK=62

Largest prime

46*365^18381-1

Attached are the results

Reserving R468, S468, and S492 to n=25K.

S472 is complete to n=25K; only k=21 & 67 are remaining; highest prime 55*472^2848+1; base released.

S476 is complete to n=25K; only k=28 is remaining; highest prime 7*476^42+1; base released. Another for the 1k thread.

This was a disappointing try at 5 consecutive proven Sierp bases. With only 3 k's remaining combined at n=3K on the final 2 of 5 bases; no primes were found for n=3K-25K. At least we got 3 consecutive, which is pretty decent on the Sierp side for such high bases.

Expectation would be to find about 1 prime from the final 3 k's remaining for n=25K-100K. With such little chance to prime all 3 and the bases so high, I'll leave that for someone else. Perhaps Max could prime the final k on base 476 like he did the Riesel side. :smile:

Results
 

Sierpinski base 332 primes found:

[code]

2*332^15+1
3*332^1+1
5*332^105+1
6*332^1+1
7*332^2+1
8*332^1+1
9*332^310+1
10*332^552+1
11*332^3+1
12*332^2+1
13*332^22+1
14*332^1+1
15*332^4+1
17*332^1327+1
18*332^6+1
19*332^14+1
20*332^31+1
21*332^4+1
22*332^10+1
23*332^269+1
24*332^3+1
25*332^2+1
26*332^61+1
27*332^4366+1
28*332^22+1
29*332^1+1
30*332^14+1
32*332^79+1
33*332^1+1
34*332^14+1
35*332^1+1
36*332^1+1
37*332^8+1
[/code]

k = 4, 16, 31 remain at n=25000. Released.

Riesel base 368 primes found:

[code]

2*368^8-1
3*368^1-1
4*368^1-1
5*368^2-1
6*368^1-1
7*368^7-1
8*368^2-1
9*368^23-1
10*368^83-1
11*368^10866-1
12*368^6-1
13*368^1-1
14*368^4-1
15*368^1-1
16*368^137-1
17*368^12-1
18*368^25-1
19*368^1-1
20*368^8-1
21*368^1-1
22*368^11-1
23*368^2204-1
24*368^1-1
25*368^1-1
26*368^6-1
27*368^2-1
28*368^1-1
29*368^8-1
30*368^9-1
31*368^3-1
32*368^15514-1
33*368^1-1
34*368^1-1
35*368^862-1
37*368^983-1
38*368^32-1
39*368^2404-1
[/code]

k=36 remains at n=25000. Released.

Sierpinski base 429 primes found:

[code]
2*429^1+1
4*429^175+1
6*429^2+1
8*429^1+1
10*429^45+1
12*429^54+1
14*429^1+1
16*429^2+1
18*429^1+1
20*429^1+1
22*429^1+1
24*429^3+1
26*429^2794+1
28*429^2+1
30*429^5+1
32*429^1+1
34*429^65+1
36*429^6+1
38*429^2+1
40*429^15+1
42*429^3+1
[/code]

Proven.

Riesel base 458 primes found:

[code]
2*458^2-1
3*458^1-1
4*458^1-1
5*458^6-1
6*458^11-1
7*458^9823-1
8*458^2-1
9*458^83-1
12*458^15-1
13*458^1-1
14*458^4-1
15*458^1-1
[/code]

k = 10 and 11 remain at n=25000. Released

More results
 

Sierspinski base 480 primes found:

[code]
2*480^8+1
3*480^3+1
4*480^2+1
5*480^29+1
6*480^5+1
7*480^1+1
8*480^2+1
9*480^2+1
10*480^1+1
11*480^1+1
13*480^50+1
14*480^18+1
15*480^2+1
16*480^1+1
17*480^1+1
18*480^1+1
19*480^2+1
20*480^1+1
21*480^6+1
22*480^7+1
23*480^7+1
24*480^4+1
25*480^5+1
26*480^2+1
27*480^14+1
28*480^1+1
29*480^1+1
30*480^1+1
31*480^4+1
32*480^1+1
33*480^2+1
34*480^2+1
35*480^3+1
36*480^3165+1
37*480^1+1
[/code]

k=12 remains at n=25000. Released.

Sierpinski base 483 primes found:

[code]

2*483^1+1
4*483^1+1
6*483^153+1
8*483^8680+1
10*483^1+1
12*483^2+1
14*483^1+1
16*483^4+1
18*483^14+1
20*483^1+1
22*483^1+1
24*483^1+1
26*483^8+1
28*483^2+1
30*483^3+1
[/code]

Proven.

R392 is complete to n=25K

CK=74

3 k's remaining k=7,28,56

No PRPs from n=2316 on (That is a first for me).

Attached are the results

Also reserving R338 to n=25K

Reserving S263.