A Sierpinski/Riesel-like problem - Page 100

sweety439 · 2020-11-18, 01:03

sweety439 · 2020-11-18, 01:05

Quote:

Originally Posted by sweety439

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 https://mersenneforum.org/showpost.p...&postcount=215

sweety439 · 2020-11-18, 01:15

GitHub link for this project: https://github.com/xayahrainie4793/E...el-conjectures (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)

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)

k <= 1024 (for b = 2 to 32 and b = 64, 128, 256)

all k <= 12 for b <= 1024

sweety439 · 2020-11-19, 03:35

Newest status: S53 at 1.67M

sweety439 · 2020-11-19, 03:39

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

Sierpinski

Riesel

sweety439 · 2020-11-21, 04:44

I have in fact completed all Sierpinski/Riesel bases 2<=b<=1024 with CK<=13 to n=6000, since I have tested all k<=12 to all Sierpinski/Riesel bases 2<=b<=1024

* 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

sweety439 · 2020-11-21, 04:48

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.

sweety439 · 2020-11-21, 04:51

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)

sweety439 · 2020-11-21, 04:52

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.

sweety439 · 2020-11-21, 04:57

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)

sweety439 · 2020-11-21, 05:01

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.

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2020-11-18, 01:03	#1090
sweety439 Nov 2016 5314₈ Posts	Sierpinski Riesel

2020-11-18, 01:15	#1092
sweety439 Nov 2016 5314₈ Posts	GitHub link for this project: https://github.com/xayahrainie4793/E...el-conjectures (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) 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) k <= 1024 (for b = 2 to 32 and b = 64, 128, 256) all k <= 12 for b <= 1024

2020-11-19, 03:35	#1093
sweety439 Nov 2016 2764₁₀ Posts	Newest status: S53 at 1.67M

2020-11-19, 03:39	#1094
sweety439 Nov 2016 2764₁₀ Posts	Conjectured k for bases 2<=b<=2500 and b = 4096, 8192, 16384, 32768, 65536 Sierpinski Riesel

2020-11-21, 04:44	#1095
sweety439 Nov 2016 2²·691 Posts	I have in fact completed all Sierpinski/Riesel bases 2<=b<=1024 with CK<=13 to n=6000, since I have tested all k<=12 to all Sierpinski/Riesel bases 2<=b<=1024 * 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

2020-11-21, 04:48	#1096
sweety439 Nov 2016 2²×691 Posts	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.

2020-11-21, 04:51	#1097
sweety439 Nov 2016 ACC₁₆ Posts	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)

2020-11-21, 04:52	#1098
sweety439 Nov 2016 ACC₁₆ Posts	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.

2020-11-21, 04:57	#1099
sweety439 Nov 2016 2²×691 Posts	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)

2020-11-21, 05:01	#1100
sweety439 Nov 2016 2764₁₀ Posts	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.