mersenneforum.org A Sierpinski/Riesel-like problem
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2022-05-05, 02:37   #1266
sweety439

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

36·5 Posts

R792 is also an interesting base, as there are many k's with algebraic factorization (combine of difference of squares and one-covering)

CK = 365, covering set = {13, 61}

tested to n=2000

Code:
(Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
for even n let k = m^2
and let n = 2*q; factors to:
(m*792^q - 1) *
(m*792^q + 1)
odd n:
factor of 13
(Condition 2):
All k where k = m^2
and m = = 11 or 50 mod 61:
for even n let k = m^2
and let n = 2*q; factors to:
(m*792^q - 1) *
(m*792^q + 1)
odd n:
factor of 61
(Condition 3):
All k where k = 22*m^2
and m = = 4 or 9 mod 13:
even n:
factor of 13
for odd n let k = 22*m^2
and let n=2*q-1; factors to:
[m*6^n*22^q - 1] *
[m*6^n*22^q + 1]
(Condition 4):
All k where k = 22*m^2
and m = = 5 or 56 mod 61:
even n:
factor of 61
for odd n let k = 22*m^2
and let n=2*q-1; factors to:
[m*6^n*22^q - 1] *
[m*6^n*22^q + 1]
k = 25, 64, 324 proven composite by condition 1.

k = 121 proven composite by condition 2.

k = 352 proven composite by condition 3.
Attached Files
 R792.txt (2.5 KB, 37 views)

2022-05-05, 02:42   #1267
sweety439

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

36×5 Posts

Quote:
 Originally Posted by sweety439 now I start R515 and R536
R515 has CK = 5 (for all bases b == 14 mod 15, 4 is both Sierpinski and Riesel, and for all bases b == 11 mod 12, 5 is both Sierpinski and Riesel)

thus this base is trivial, only k = 1 through k = 4 need primes, however, only k = 3 has an easy prime (n<1000).

Code:
1,2243
2,58466
3,68
4,1579
Note that R515 has no single prime with n <= 60 (I doubt whether it is the smallest such base ... but this needs to check)

 2022-05-19, 00:30 #1268 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36·5 Posts Take the following bases: R165 R178 (k=19) R186
2022-05-19, 20:13   #1269
sweety439

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

36×5 Posts

Quote:
 Originally Posted by sweety439 Take the following bases: R165 R178 (k=19) R186
All tested to n=6K, no prime or PRP found

bases released, reserve R181 (k=21)

2022-06-22, 03:08   #1270
sweety439

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

E3D16 Posts

Quote:
 Originally Posted by sweety439 Take the following bases: R165 R178 (k=19) R186
R165 at n=15K
R186 at n=13K

 2022-06-25, 14:20 #1271 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36×5 Posts R178 update k=19 has PRP at n=13655 k=4 remains at n=13K, continuing .... update for R85, k=61 at n=11K Last fiddled with by sweety439 on 2022-07-23 at 07:20
 2022-07-31, 20:53 #1272 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36·5 Posts status update: R85 at n=15K R31 k=5 at n=30K
 2022-08-01, 21:55 #1273 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36×5 Posts R181 k=21 at n=12K reserve R181 k=5
 2022-08-05, 13:22 #1274 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36×5 Posts R181 k=5 at n=21000, no prime or PRP Reserve S103 (k=7)
 2022-08-07, 02:46 #1275 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36×5 Posts S103 k=7 at n=22000, no primes or PRPs
 2022-08-07, 03:05 #1276 sweety439     "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 36·5 Posts All 1k bases (I have a plan to reserve all of them to 20K+ or 30K+) Code: base remain k test limit of n S12 12 33.55M S18 18 33.55M S25 71 10K S32 4 1.717G S37 37 524K S38 1 16.77M S50 1 16.77M S53 4 2M S55 1 524K S62 1 16.77M S72 72 16.77M S77 1 524K S89 1 524K S91 1 524K S92 1 16.77M S98 1 16.77M S99 1 524K S103 7 22K S104 1 16.77M S107 1 524K S109 1 524K S113 17 8K S118 48 740K S140 8 1M S143 1 524K S144 1 16.77M S149 1 524K S151 1 524K S160 20 2K S165 43 2K S174 4 1M S176 55 2K S179 1 524K S189 1 524K S191 3 6K S197 1 524K R43 13 50K R70 811 50K R85 61 15K R94 29 1M R97 22 35.8K R118 43 37K R123 11 8K R165 65 15K R173 11 6K R178 4 13K R185 1 66.3K R186 36 13K

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