[QUOTE=sweety439;460416]The 1st, 2nd and 3rd conjecture of Sierpinski/Riesel bases 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 31 and 32 are:

[CODE]
base 1st 2nd 3rd
S17 31 47 127
S18 398 512 571
S19 9 11 29
S20 8 13 29
S21 23 43 47
S23 5 7 17
S25 79 103 185
S26 221 284 1627
S27 13 15 41
S29 4 7 11
S31 239 293 521
S32 10 23 43
R17 49 59 65
R18 246 664 723
R19 9 11 29
R20 8 13 29
R21 45 65 133
R23 5 7 17
R25 105 129 211
R26 149 334 1892
R27 13 15 41
R29 4 9 11
R31 145 265 443
R32 10 23 43
[/CODE][/QUOTE]

Update files for the Sierpinski 1st, 2nd and 3rd problem for bases 17 to 21.

S17 has k=53 remain.
S18 has k=18 remain. (k=324 will have the same prime as k=18)
S19, S20 and S21 are proven.

[QUOTE=sweety439;460416]The 1st, 2nd and 3rd conjecture of Sierpinski/Riesel bases 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 31 and 32 are:

[CODE]
base 1st 2nd 3rd
S17 31 47 127
S18 398 512 571
S19 9 11 29
S20 8 13 29
S21 23 43 47
S23 5 7 17
S25 79 103 185
S26 221 284 1627
S27 13 15 41
S29 4 7 11
S31 239 293 521
S32 10 23 43
R17 49 59 65
R18 246 664 723
R19 9 11 29
R20 8 13 29
R21 45 65 133
R23 5 7 17
R25 105 129 211
R26 149 334 1892
R27 13 15 41
R29 4 9 11
R31 145 265 443
R32 10 23 43
[/CODE][/QUOTE]

Update files for S23, S25, S27 and S29. (since S31 is a low-weight base, unlike S18 is a high-weight base, I didn't reserve it)

S23 and S29 are proven.
S25 has k=71 and k=181 remain. (the search for S25 k=181 is completely the same as the search for S5 k=181)
S27 has k=33 remain.

[QUOTE=sweety439;460416]The 1st, 2nd and 3rd conjecture of Sierpinski/Riesel bases 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 31 and 32 are:

[CODE]
base 1st 2nd 3rd
S17 31 47 127
S18 398 512 571
S19 9 11 29
S20 8 13 29
S21 23 43 47
S23 5 7 17
S25 79 103 185
S26 221 284 1627
S27 13 15 41
S29 4 7 11
S31 239 293 521
S32 10 23 43
R17 49 59 65
R18 246 664 723
R19 9 11 29
R20 8 13 29
R21 45 65 133
R23 5 7 17
R25 105 129 211
R26 149 334 1892
R27 13 15 41
R29 4 9 11
R31 145 265 443
R32 10 23 43
[/CODE][/QUOTE]

Update files for the Riesel 1st, 2nd and 3rd problem for bases 17 to 21.

R17, R19, R20 and R21 are proven.
R18 has k=533, 597 and 628 remain. (Note that for k=324, the (probable) prime is the smallest repunit (probable) prime with at least 3 1s in base 18: (18^25667-1)/17 = (324*18^25665-1)/gcd(324-1,18-1)), see [URL="http://oeis.org/A128164"]http://oeis.org/A128164[/URL].

[QUOTE=sweety439;460416]The 1st, 2nd and 3rd conjecture of Sierpinski/Riesel bases 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 31 and 32 are:

[CODE]
base 1st 2nd 3rd
S17 31 47 127
S18 398 512 571
S19 9 11 29
S20 8 13 29
S21 23 43 47
S23 5 7 17
S25 79 103 185
S26 221 284 1627
S27 13 15 41
S29 4 7 11
S31 239 293 521
S32 10 23 43
R17 49 59 65
R18 246 664 723
R19 9 11 29
R20 8 13 29
R21 45 65 133
R23 5 7 17
R25 105 129 211
R26 149 334 1892
R27 13 15 41
R29 4 9 11
R31 145 265 443
R32 10 23 43
[/CODE][/QUOTE]

Update files for R23, R25, R27 and R29. (since R31 is a low-weight base, unlike S18 is a high-weight base, I didn't reserve it)

R23, R27 and R29 are proven.
R25 has k=181 remain. (Interestingly, S25 also has k=181 remain)

[QUOTE=sweety439;469197]S12 has 9 k's remain:

12, 563, 846, 885, 911, 976, 1041, 1052, 1057. (k = 144 is included in the conjectures but excluded from testing, since this k-value will have the same prime as k = 12)

Since 563*12^4020+1 is prime, k=563 can be removed, I will run other k's (except k=12) after the reservations for S10 were done (see post [URL="http://mersenneforum.org/showpost.php?p=469196&postcount=469"]#469[/URL]).[/QUOTE]

1052*12^5715+1 and 1057*12^690+1 are primes.

Thus S12 now only has these k's remain:

12, 846, 885, 911, 976, 1041

[QUOTE=sweety439;490255]1052*12^5715+1 and 1057*12^690+1 are primes.

Thus S12 now only has these k's remain:

12, 846, 885, 911, 976, 1041[/QUOTE]

(846*12^1384+1)/11 is prime.

Thus S12 now only has these k's remain:

12, 885, 911, 976, 1041

Update files for 1st, 2nd and 3rd conjectures for S32, S64, S128 and S256.

Note:

Covering set for (98*128^n+1)/gcd(98+1,128-1): {3, 5, 113}
Covering set for (467*256^n+1)/gcd(467+1,256-1): {3, 7, 241}

[QUOTE=sweety439;490273]Update files for 1st, 2nd and 3rd conjectures for S32, S64, S128 and S256.

Note:

Covering set for (98*128^n+1)/gcd(98+1,128-1): {3, 5, 113}
Covering set for (467*256^n+1)/gcd(467+1,256-1): {3, 7, 241}[/QUOTE]

Remain k's:

S32: 4, 16
S64: none (proven)
S128: 16, 40, 47, 83, 88, 94
S256: 89, 116, 215, 230, 263, 281, 309, 329, 368, 383, 398, 407, 434, 449, 459

1st, 2nd and 3rd CK:

S32: 10, 23, 43
S64: 14, 51, 79
S128: 44, 85, 98
S256: 38, 194, 467
R32: 10, 23, 43
R64: 14, 51, 79
R128: 44, 59, 85
R256: 100, 172, 211

Update files for 1st, 2nd and 3rd conjectures for R32, R64, R128 and R256.

[QUOTE=sweety439;490276]Update files for 1st, 2nd and 3rd conjectures for R32, R64, R128 and R256.[/QUOTE]

Remain k's:

R32: 29
R64: none (proven)
R128: 46
R256: 191