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Old 2016-12-23, 12:28   #23
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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
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Old 2016-12-23, 14:05   #24
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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
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Old 2016-12-23, 18:16   #25
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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!!!
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Old 2016-12-23, 18:19   #26
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Update the complete text file for the conjectured smallest strong (extended) k to all bases 2<=b<=64.
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Old 2016-12-23, 18:56   #27
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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
File Type: txt extend-Sierp-base13.txt (77 Bytes, 75 views)
File Type: txt extend-Sierp-base14.txt (15 Bytes, 72 views)
File Type: txt extend-Sierp-base16.txt (216 Bytes, 67 views)
File Type: txt extend-Sierp-base17.txt (179 Bytes, 67 views)
File Type: txt extend-Sierp-base18.txt (2.7 KB, 129 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:02
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Old 2016-12-23, 18:58   #28
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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
File Type: txt extend-Sierp-base19.txt (42 Bytes, 77 views)
File Type: txt extend-Sierp-base20.txt (36 Bytes, 76 views)
File Type: txt extend-Sierp-base21.txt (124 Bytes, 72 views)
File Type: txt extend-Sierp-base23.txt (22 Bytes, 75 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:11
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Old 2016-12-23, 18:59   #29
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Also running extended Riesel conjectures.
Attached Files
File Type: txt extend-Riesel-base13.txt (162 Bytes, 68 views)
File Type: txt extend-Riesel-base14.txt (15 Bytes, 70 views)
File Type: txt extend-Riesel-base16.txt (633 Bytes, 71 views)
File Type: txt extend-Riesel-base17.txt (292 Bytes, 74 views)
File Type: txt extend-Riesel-base18.txt (1.6 KB, 67 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:01
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Old 2016-12-23, 19:00   #30
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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
File Type: txt extend-Riesel-base19.txt (47 Bytes, 71 views)
File Type: txt extend-Riesel-base20.txt (36 Bytes, 69 views)
File Type: txt extend-Riesel-base21.txt (258 Bytes, 72 views)
File Type: txt extend-Riesel-base23.txt (20 Bytes, 69 views)

Last fiddled with by sweety439 on 2016-12-23 at 19:01
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Old 2016-12-23, 19:14   #31
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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
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Old 2016-12-23, 19:43   #32
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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
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Old 2016-12-24, 19:02   #33
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Found the probable prime (29*17^4904-1)/4.

Extended R17 is proven!!!
Attached Files
File Type: txt extend-Riesel-base17.txt (265 Bytes, 78 views)
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