A Sierpinski/Riesel-like problem

[sweety439]

From the thread https://mersenneforum.org/showthread...=10354&page=10, searched up to n=6000, k=4 and k=5 (for the Riesel side) are still running ....

[sweety439]

All searched up to n=2^12

Riesel k=4, Sierp k=4, Sierp k=5, Sierp k=6 are still running

[sweety439]

Exclusions for k<=12:

Riesel k=1:
b=m^r with r>1 proven composite by full algebraic factors

Riesel k=2:
none

Riesel k=3:
none

Riesel k=4:
b==(4 mod 5): odd n, factor of 5; even n, algebraic factors
b=m^2 proven composite by full algebraic factors

Riesel k=5:
b==(11 mod 12): covering set [2, 3]

Riesel k=6:
b==(34 mod 35): covering set [5, 7]
b=6*m^2 with m==(2, 3 mod 5): even n, factor of 5; odd n, algebraic factors

Riesel k=7:
b==(11 mod 12): covering set [2, 3]

Riesel k=8:
b==(20 mod 21): covering set [3, 7]
b==(83, 307 mod 455): covering set [5, 7, 13]
b=m^3 proven composite by full algebraic factors

Riesel k=9:
b==(4 mod 5): odd n, factor of 5; even n, algebraic factors
b==(9 mod 16): odd n, factor of 2; even n, algebraic factors
b=m^2 proven composite by full algebraic factors

Riesel k=10:
b==(32 mod 33): covering set [3, 11]

Riesel k=11:
b==(14 mod 15): covering set [3, 5]
b==(19 mod 20): covering set [2, 5]
b=11*m^2 with m==(2, 3 mod 5): even n, factor of 5; odd n, algebraic factors

Riesel k=12:
b==(142 mod 143): covering set [11, 13]
base 307: covering set [5, 11, 29]
base 901: covering set [7, 11, 13, 19]

Sierp k=1:
b=m^r with odd r>1 proven composite by full algebraic factors

Sierp k=2:
none

Sierp k=3:
none

Sierp k=4:
b==(14 mod 15); covering set [3, 5]
b=m^4 proven composite by full algebraic factors

Sierp k=5:
b==(11 mod 12): covering set [2, 3]

Sierp k=6:
b==(34 mod 35); covering set [5, 7]

Sierp k=7:
b==(5, 11, 23 mod 24): covering set [2, 3]

Sierp k=8:
b==(20 mod 21): covering set [3, 7]
b==(47, 83 mod 195): covering set [3, 5, 13]
base 467: covering set [3, 5, 7, 19, 37]
base 722: covering set [3, 5, 13, 73, 109]
b=m^3 proven composite by full algebraic factors
base 128: no possible prime

Sierp k=9:
b==(19 mod 20): covering set [2, 5]

Sierp k=10:
b==(32 mod 33): covering set [3, 11]

Sierp k=11:
b==(14 mod 15): covering set [3, 5]
b==(19 mod 20): covering set [2, 5]
b==(5 mod 24): covering set [2, 3]

Sierp k=12:
b==(142 mod 143): covering set [11, 13]
bases 296 and 901: covering set [7, 11, 13, 19]
bases 562, 828, 900, and 1166: covering set [7, 13, 19]
base 563 and 1433: covering set [5, 7, 13, 19, 29]
base 597: covering set [5, 13, 29]

[sweety439]

Update files.

[sweety439]

Primality certificates for the primes >= 300 digits for the proven or near-proven bases for the k such that gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not 1: (only for k < 1st CK)

S7:

k=141

S13:

k=11 (proven by N-1-method)

S16:

k=23

S25:

k=61

S33: (k=319 and k=407 are only probable primes)

k=11
k=31 (proven by N-1-method)
k=63
k=251
k=305

S36:

k=223 (proven by N+1-method) (certificate for large prime factor for N+1)
k=1000
k=1669

S37:

k=19

S43:

k=9
k=13 (proven by N-1-method)

[sweety439]

S46: (k=17 is only probable prime)

k=89
k=95
k=140
k=229
k=278
k=347
k=551
k=619
k=729

S58: (k=266 is only probable prime)

k=20
k=29
k=53
k=146
k=209
k=296
k=332
k=362
k=383
k=392
k=416

S61:

k=23
k=43
k=62

S64:

k=11

[sweety439]

Originally Posted by sweety439

Update files.

Update files, all Sierp/Riesel k=1~7 (for bases 2<=b<=1024) are searched to n=6000

[sweety439]

Originally Posted by sweety439

S46: (k=17 is only probable prime)

k=89
k=95
k=140
k=229
k=278
k=347
k=551
k=619
k=729

S58: (k=266 is only probable prime)

k=20
k=29
k=53
k=146
k=209
k=296
k=332
k=362
k=383
k=392
k=416

S61:

k=23
k=43
k=62

S64:

k=11

S67:

k=11

S72:

k=141

S73: (k=14 is only probable prime)

k=21
k=39

S75:

k=11

S79:

k=3 (proven by N+1-method) (certificate for large prime factor for N+1)
k=5 (proven by N-1-method)

S80:

k=552

S81: (k=311 is only probable prime)

k=34
k=41
k=43
k=317
k=349
k=389
k=415
k=425
k=431
k=433
k=479
k=503

S88:

k=8

S92:

k=25

S93: (k=19 is only probable prime)

k=3 (proven by N-1-method)
k=31
k=43

S94:

k=17

S97:

k=26
k=68
k=87
k=122

S103: (k=13 is only probable prime)

k=20

S105: (k=191 is only probable prime)

k=39
k=183

S107:

k=3 (proven by N+1-method)

S113:

k=13

S115:

k=50

[sweety439]

S117:

k=11
k=47
k=67
k=75
k=77
k=81 (proven by N+1-method)

S256: (k=11 is only probable prime)

k=23

S1024:

k=14
k=41
k=44

[sweety439]

https://docs.google.com/document/d/e...ZJlsvnJhll/pub

Update newest file for Riesel problems to include R126

[sweety439]

Reserve R70