A Sierpinski/Riesel-like problem - Page 3

sweety439 · 2016-12-23, 12:28

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.

sweety439 · 2016-12-23, 14:05

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.

sweety439 · 2016-12-23, 18:16

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!!!

sweety439 · 2016-12-23, 18:19

Update the complete text file for the conjectured smallest strong (extended) k to all bases 2<=b<=64.

sweety439 · 2016-12-23, 18:56

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.

sweety439 · 2016-12-23, 18:58

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.

sweety439 · 2016-12-23, 18:59

Also running extended Riesel conjectures.

sweety439 · 2016-12-23, 19:00

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?

sweety439 · 2016-12-23, 19:14

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?

sweety439 · 2016-12-23, 19:43

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.

sweety439 · 2016-12-24, 19:02

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

Extended R17 is proven!!!

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. (3379136^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, 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 ((1977^n-1)/2) S10, k=269 ((26910^n+1)/9) R17, k=29 ((2917^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

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
The dual Sierpinski/Riesel problem	sweety439	sweety439	15	2022-01-26 23:43
Semiprime and n-almost prime candidate for the k's with algebra for the Sierpinski/Riesel problem	sweety439	sweety439	11	2020-09-23 01:42
The reverse Sierpinski/Riesel problem	sweety439	sweety439	20	2020-07-03 17:22
Sierpinski/ Riesel bases 6 to 18	robert44444uk	Conjectures 'R Us	139	2007-12-17 05:17
Sierpinski/Riesel Base 10	rogue	Conjectures 'R Us	11	2007-12-17 05:08

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!!!