20220505, 02:37  #1266 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3577_{10} Posts 
R792 is also an interesting base, as there are many k's with algebraic factorization (combine of difference of squares and onecovering)
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*q1; 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*q1; factors to: [m*6^n*22^q  1] * [m*6^n*22^q + 1] k = 121 proven composite by condition 2. k = 352 proven composite by condition 3. 
20220505, 02:42  #1267 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
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 
20220519, 00:30  #1268 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Take the following bases:
R165 R178 (k=19) R186 
20220519, 20:13  #1269 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 

20220622, 03:08  #1270 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 

20220625, 14:20  #1271 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 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 20220723 at 07:20 
20220731, 20:53  #1272 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
DF9_{16} Posts 
status update:
R85 at n=15K R31 k=5 at n=30K 
20220801, 21:55  #1273 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
R181 k=21 at n=12K
reserve R181 k=5 
20220805, 13:22  #1274 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
DF9_{16} Posts 
R181 k=5 at n=21000, no prime or PRP
Reserve S103 (k=7) 
20220807, 02:46  #1275 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
3577_{10} Posts 
S103 k=7 at n=22000, no primes or PRPs

20220807, 03:05  #1276 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
DF9_{16} 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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