20161223, 12:28  #23 
Nov 2016
2,267 Posts 
Found more conjectured k for the extended Sierpinski/Riesel problems:
S24: 30651 S42: 13372 S60: 16957 R24: 32336 R42: 15137 R60: 20558 The six conjectured k's are the same as the conjectured k's for the original Sierpinski/Riesel problem. Thus, for base 24, base 42 and base 60 (but not for all bases), the extend Sierpinski/Riesel problem covers the original Sierpinski/Riesel problem. Last fiddled with by sweety439 on 20161223 at 12:28 
20161223, 14:05  #24 
Nov 2016
4333_{8} Posts 
Found the conjectured k for R36: 33791.
(33791*36^n1)/5 has a cover set: {13, 31, 43, 97}. Now, I still found no k with a cover set only for these bases <= 64: S15, S40, S52. R15, R40, R52. Last fiddled with by sweety439 on 20161223 at 14:07 
20161223, 18:16  #25 
Nov 2016
2,267 Posts 
Found more conjectured k for the extended Sierpinski/Riesel problems:
S15: 673029 cover: {2, 17, 113, 1489} period=8 S40: 47723 cover: {3, 7, 41, 223} period=6 S52: 28674 cover: {5, 53, 541} period=4 R15: 622403 cover: {2, 17, 113, 1489} period=8 R40: 25462 cover: {3, 7, 41, 223} period=6 R52: 25015 cover: {3, 7, 53, 379} period=6 Now, the list of the conjectured smallest strong (extended) Sierpinski/Riesel number for bases 2<=b<=64 is completed!!! 
20161223, 18:19  #26 
Nov 2016
2,267 Posts 
Update the complete text file for the conjectured smallest strong (extended) k to all bases 2<=b<=64.

20161223, 18:56  #27 
Nov 2016
2,267 Posts 
Now, I am running the extended Sierpinski/Riesel conjectures for 13<=b<=24. Since the conjectured k for base 15, 22 and 24 (on both sides) are larger, I only run other bases.
Last fiddled with by sweety439 on 20161223 at 19:02 
20161223, 18:58  #28 
Nov 2016
2,267 Posts 
All extended Sierpinski conjectures I ran are proven. (S18 is proven since only GFNs (18*18^n+1 and 324*18^n+1) are remain)
Define of GFNs: Only exist for extended Sierpinski conjectures ((k*b^n+1)/gcd(k+1,b1)). gcd(k+1,b1)=1. k is a rational power of b. Thus, 100*10^n+1, 18*18^n+1 and 4*32^n+1 are GFNs, but 4*155^n+1, (25*5^n+1)/2 and (7*49^n+1)/8 are not. Last fiddled with by sweety439 on 20161223 at 19:11 
20161223, 18:59  #29 
Nov 2016
2,267 Posts 
Also running extended Riesel conjectures.
Last fiddled with by sweety439 on 20161223 at 19:01 
20161223, 19:00  #30 
Nov 2016
2,267 Posts 
All extended Riesel conjectures I ran are proven except R17, R17 has only k=29 remain.
Can someone find a prime of the form (29*17^n1)/4? Last fiddled with by sweety439 on 20161223 at 19:01 
20161223, 19:14  #31 
Nov 2016
2,267 Posts 
The extended Sierpinski/Riesel conjectures for bases 2<=b<=24 with only one k remain:
R7, k=197 ((197*7^n1)/2) S10, k=269 ((269*10^n+1)/9) R17, k=29 ((29*17^n1)/4) Can you find the smallest n? Last fiddled with by sweety439 on 20161223 at 19:15 
20161223, 19:43  #32 
Nov 2016
2,267 Posts 
List of the status for the extended Sierpinski/Riesel conjectures to bases 2<=b<=24: (the number of remain k does not contain the k excluded from testing, i.e. k's that is multiple of b and (k+1)/gcd(k+1, b1) are composite, and also not contain GFN's)
S2: conjectured k=78557, 5 k's remain (21181, 22699, 24747, 55459, 67607) S3: conjectured k=11047, not completely started. S4: conjectured k=419, proven. S5: conjectured k=7, proven. S6: conjectured k=174308, not completely started. S7: conjectured k=209, proven. S8: conjectured k=47, proven. S9: conjectured k=31, proven. S10: conjectured k=989, only k=269 remain. S11: conjectured k=5, proven. S12: conjectured k=521, proven. S13: conjectured k=15, proven. S14: conjectured k=4, proven. S15: conjectured k=673029, not completely started. S16: conjectured k=38, proven. S17: conjectured k=31, proven. S18: conjectured k=398, proven. S19: conjectured k=9, proven. S20: conjectured k=8, proven. S21: conjectured k=23, proven. S22: conjectured k=2253, not completely started. S23: conjectured k=5, proven. S24: conjectured k=30651, not completely started. R2: conjectured k=509203, 52 k's remain (2293, 9221, 23669, 31859, 38473, 46663, 67117, 74699, 81041, 93839, 97139, 107347, 121889, 129007, 143047, 146561, 161669, 192971, 206039, 206231, 215443, 226153, 234343, 245561, 250027, 273809, 315929, 319511, 324011, 325123, 327671, 336839, 342847, 344759, 351134, 362609, 363343, 364903, 365159, 368411, 371893, 384539, 386801, 397027, 409753, 444637, 470173, 474491, 477583, 478214, 485557, 494743) R3: conjectured k=12119, 15 k's remain (1613, 1831, 1937, 3131, 3589, 5755, 6787, 7477, 7627, 7939, 8713, 8777, 9811, 10651, 11597) R4: conjectured k=361, proven. R5: conjectured k=13, proven. R6: conjectured k=84687, 13 k's remain (1597, 2626, 6236, 9491, 37031, 49771, 50686, 53941, 55061, 57926, 76761, 79801, 83411) R7: conjectured k=457, only k=197 remain. R8: conjectured k=14, proven. R9: conjectured k=41, proven. R10: conjectured k=334, proven. R11: conjectured k=5, proven. R12: conjectured k=376, proven. R13: conjectured k=29, proven. R14: conjectured k=4, proven. R15: conjectured k=622403, not completely started. R16: conjectured k=100, proven. R17: conjectured k=49, only k=29 remain. R18: conjectured k=246, proven. R19: conjectured k=9, proven. R20: conjectured k=8, proven. R21: conjectured k=45, proven. R22: conjectured k=2738, not completely started. R23: conjectured k=5, proven. R24: conjectured k=32336, not completely started. Last fiddled with by sweety439 on 20170203 at 17:24 
20161224, 19:02  #33 
Nov 2016
2,267 Posts 
Found the probable prime (29*17^49041)/4.
Extended R17 is proven!!! 
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