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 2016-12-23, 12:28 #23 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 356710 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 2016-12-23 at 12:28
 2016-12-23, 14:05 #24 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 3×29×41 Posts Found the conjectured k for R36: 33791. (33791*36^n-1)/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 2016-12-23 at 14:07
 2016-12-23, 18:16 #25 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 DEF16 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!!!
 2016-12-23, 18:19 #26 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 67578 Posts Update the complete text file for the conjectured smallest strong (extended) k to all bases 2<=b<=64. Attached Files
2016-12-23, 18:56   #27
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

1101111011112 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.
Attached Files
 extend-Sierp-base13.txt (77 Bytes, 214 views) extend-Sierp-base14.txt (15 Bytes, 205 views) extend-Sierp-base16.txt (216 Bytes, 196 views) extend-Sierp-base17.txt (179 Bytes, 198 views) extend-Sierp-base18.txt (2.7 KB, 262 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:02

2016-12-23, 18:58   #28
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

67578 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,b-1)).
gcd(k+1,b-1)=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.
Attached Files
 extend-Sierp-base19.txt (42 Bytes, 204 views) extend-Sierp-base20.txt (36 Bytes, 205 views) extend-Sierp-base21.txt (124 Bytes, 203 views) extend-Sierp-base23.txt (22 Bytes, 198 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:11

2016-12-23, 18:59   #29
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3×29×41 Posts

Also running extended Riesel conjectures.
Attached Files
 extend-Riesel-base13.txt (162 Bytes, 194 views) extend-Riesel-base14.txt (15 Bytes, 197 views) extend-Riesel-base16.txt (633 Bytes, 205 views) extend-Riesel-base17.txt (292 Bytes, 193 views) extend-Riesel-base18.txt (1.6 KB, 203 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:01

2016-12-23, 19:00   #30
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3×29×41 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^n-1)/4?
Attached Files
 extend-Riesel-base19.txt (47 Bytes, 192 views) extend-Riesel-base20.txt (36 Bytes, 203 views) extend-Riesel-base21.txt (258 Bytes, 202 views) extend-Riesel-base23.txt (20 Bytes, 190 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:01

 2016-12-23, 19:14 #31 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 3×29×41 Posts The extended Sierpinski/Riesel conjectures for bases 2<=b<=24 with only one k remain: R7, k=197 ((197*7^n-1)/2) S10, k=269 ((269*10^n+1)/9) R17, k=29 ((29*17^n-1)/4) Can you find the smallest n? Last fiddled with by sweety439 on 2016-12-23 at 19:15
 2016-12-23, 19:43 #32 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 1101111011112 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, b-1) 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 2017-02-03 at 17:24
2016-12-24, 19:02   #33
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

3×29×41 Posts

Found the probable prime (29*17^4904-1)/4.

Extended R17 is proven!!!
Attached Files
 extend-Riesel-base17.txt (265 Bytes, 199 views)

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