20161223, 12:28  #23 
Nov 2016
B04_{16} 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
2^{2}×3×5×47 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^{2}×3×5×47 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^{2}×3×5×47 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^{2}·3·5·47 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^{2}·3·5·47 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^{2}·3·5·47 Posts 
Also running extended Riesel conjectures.
Last fiddled with by sweety439 on 20161223 at 19:01 
20161223, 19:00  #30 
Nov 2016
2^{2}·3·5·47 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^{2}×3×5×47 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^{2}×3×5×47 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^{2}·3·5·47 Posts 
Found the probable prime (29*17^49041)/4.
Extended R17 is proven!!! 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The dual Sierpinski/Riesel problem  sweety439  sweety439  14  20210215 15:58 
Semiprime and nalmost prime candidate for the k's with algebra for the Sierpinski/Riesel problem  sweety439  sweety439  11  20200923 01:42 
The reverse Sierpinski/Riesel problem  sweety439  sweety439  20  20200703 17:22 
Sierpinski/ Riesel bases 6 to 18  robert44444uk  Conjectures 'R Us  139  20071217 05:17 
Sierpinski/Riesel Base 10  rogue  Conjectures 'R Us  11  20071217 05:08 