[URL="https://docs.google.com/document/d/e/2PACX-1vTl-BpXPFJQRagEzz0vEwPIqKoj7tV9_qU7xsi_iAET3W9du_OrWWDHGzthWbwwstBhML2_a2t3LQfX/pub"]Sierpinski[/URL]

[URL="https://docs.google.com/document/d/e/2PACX-1vRoFRaTy4zA17OR91gL64LaGt6XnVklfN8Y5gHwBjv8nyfq211dkKHwH9_vFKR76O79IcTJ0ww09n2c/pub"]Riesel[/URL]

[QUOTE=sweety439;563579][URL="https://docs.google.com/document/d/e/2PACX-1vTl-BpXPFJQRagEzz0vEwPIqKoj7tV9_qU7xsi_iAET3W9du_OrWWDHGzthWbwwstBhML2_a2t3LQfX/pub"]Sierpinski[/URL]

[URL="https://docs.google.com/document/d/e/2PACX-1vRoFRaTy4zA17OR91gL64LaGt6XnVklfN8Y5gHwBjv8nyfq211dkKHwH9_vFKR76O79IcTJ0ww09n2c/pub"]Riesel[/URL][/QUOTE]

Updating:

* S36 k=1814 tested to n=100K (the same testing: S6 k=1814 tested to n=200K)
* R43 tested to n=50K by Dylan14
* R70 tested to n=50K
* 146561*2^11280802-1 is prime found by PrimeGrid's project, see post [URL="https://mersenneforum.org/showpost.php?p=563554&postcount=215"]https://mersenneforum.org/showpost.php?p=563554&postcount=215[/URL]

GitHub link for this project: [URL="https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures[/URL] (for b = 2 to 128 and b = 256, 512, 1024, with k < 1st CK)

GitHub link for the (k,b) combo outside of this project: (including b > 128 (except b = 256, 512, 1024) and k's > CK)

[URL="https://github.com/xayahrainie4793/first-4-Sierpinski-Riesel-conjectures"]k < 4th CK (for b = 2 to 64 (except 2, 3, 6, 15, 22, 24, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63 (which have larger conjectured k's)) and b = 100, 128, 256, 512, 1024)[/URL]

[URL="https://github.com/xayahrainie4793/all-k-1024"]k <= 1024 (for b = 2 to 32 and b = 64, 128, 256)[/URL]

[URL="https://github.com/xayahrainie4793/Sierpinski-Riesel-for-fixed-k-and-variable-base"]all k <= 12 for b <= 1024[/URL]

Newest status: S53 at 1.67M

Conjectured k for bases 2<=b<=2500 and b = 4096, 8192, 16384, 32768, 65536

[URL="https://raw.githubusercontent.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/master/Sierpinski%20CK%20for%20bases%20up%20to%202048.txt"]Sierpinski[/URL]

[URL="https://raw.githubusercontent.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures/master/Riesel%20CK%20for%20bases%20up%20to%202048.txt"]Riesel[/URL]

I have in fact completed all Sierpinski/Riesel bases 2<=b<=1024 with CK<=13 to n=6000, since [URL="https://github.com/xayahrainie4793/Sierpinski-Riesel-for-fixed-k-and-variable-base"]I have tested all k<=12 to all Sierpinski/Riesel bases 2<=b<=1024[/URL]

* Sierpinski bases 2<=b<=1024 have CK=4 if and only if b == 14 mod 15

* Riesel bases 2<=b<=1024 have CK=4 if and only if b == 14 mod 15

* Sierpinski bases 2<=b<=1024 have CK=5 if and only if b == 11 mod 12

* Riesel bases 2<=b<=1024 have CK=5 if and only if b == 11 mod 12

* Sierpinski bases 2<=b<=1024 have CK=6 if and only if b == 34 mod 35

* Riesel bases 2<=b<=1024 have CK=6 if and only if b == 34 mod 35

For the Riesel bases with CK=4:

R269 has k=1 remain
R659 has k=3 remain
R1019 has k=2 remain

Other bases are proven.

For the Riesel bases with CK=5:

bases 347, 575, 587, 731 have k=3 remain
bases 275 and 647 have k=4 remain

Other bases are proven (an interesting one is R311, largest (probable) prime is (1*311^36497-1)/gcd(1-1,311-1) = (311^36497-1)/310, for k=1)

For the Riesel bases with CK=6:

R384 has k=1 remain
R489 has k=5 remain
R699 has k=3 remain

Other bases are proven.

For the Sierpinski bases with CK=4:

bases 89, 104, 149, 179, 269, 344, 359, 389, 404, 509, 524, 629, 659, 734, 749, 794, 809, 854, 899, 944, 974 have k=1 remain
bases 914 and 1004 have k=2 remain
bases 779 has k=3 remain

Other bases are proven (interestingly, all Sierpinski bases with CK=4 have at most one k remain, i.e. there are no Sierpinski bases with CK=4 which are 2k bases or 3k bases)

For the Sierpinski bases with CK=5:

bases 83, 107, 143, 155, 215, 227, 263, 287, 311, 347, 383, 407, 443, 467, 515, 563, 611, 635, 647, 671, 683, 707, 731, 743, 755, 767, 851, 887, 911, 923, 947, 983 have k=1 remain
bases 83, 191, 323, 683, 743, 827 have k=3 remain
bases 155, 335, 371, 395, 467, 611, 731, 767, 803, 851, 875, 971 have k=4 remain

Other bases are proven.