A Sierpinski/Riesel-like problem - Page 51

MisterBitcoin · 2018-01-06, 15:05

I would be very happy if you would post an list with every PRP you found in your project. (sorted by base please)
I´m willing to test some of those PRP´s with primo, like I did on (6^1189*5741-1)/5, which is prime.

sweety439 · 2018-01-06, 19:46

Quote:

Originally Posted by MisterBitcoin

I would be very happy if you would post an list with every PRP you found in your project. (sorted by base please)
I´m willing to test some of those PRP´s with primo, like I did on (6^1189*5741-1)/5, which is prime.

There are some PRPs which if you prove them to be prime, then you will fully prove the bases.

S61:

(43*61^2788+1)/4
(62*61^3698+1)/3

S64:

(11*64^3222+1)/3

S75:

(11*75^3071+1)/2

S105:

(191*105^5045+1)/8

S256:

(11*256^5702+1)/3

R7: (the probable prime of k = 197 and 367 of this base are too large, please do not prove the primility of them :-) )

(159*7^4896-1)/2
(313*7^5907-1)/6
(367*7^15118-1)/6
(197*7^181761-1)/2

R17:

(29*17^4904-1)/4

R51:

(1*51^4229-1)/50

R67:

(25*67^2829-1)/6

R91:

(1*91^4421-1)/90
(27*91^5048-1)/2

R100:

(133*100^5496-1)/33

R107:

(3*107^4900-1)/2

R121:

(79*121^4545-1)/6

I suggest you to prove the primility of them first.

sweety439 · 2018-01-06, 19:58

Quote:

Originally Posted by MisterBitcoin

I would be very happy if you would post an list with every PRP you found in your project. (sorted by base please)
I´m willing to test some of those PRP´s with primo, like I did on (6^1189*5741-1)/5, which is prime.

Also, PRPs for the unproven bases (not include the bases with so many k's remain):

(61*25^3104+1)/2 (S25 still has k=71 remain)
(189*31^5570+1)/10 (S31 still has 10 k's remain)
(319*33^5043+1)/32
(407*33^10961+1)/8 (S33 still has k=67 and k=203 remain)
(19*37^5310+1)/4 (S37 still has k=37 remain)
(311*81^7834+1)/8 (S81 still has 10 k's remain)
(13*103^7010+1)/2 (S103 still has k=7 remain)
(44*1024^1933+1)/3 (S1024 still has 5 k's remain)

(1654*30^38869-1)/29 (it is too large, please do not prove the primility of them :-) ) (R30 still has 9 k's remain)
(77*61^3080-1)/4
(13*61^4134-1)/12 (R61 still has 3 k's remain)
(4*115^4223-1)/3 (R115 still has 5 k's remain)
(13*1024^1167-1)/3
(43*1024^2290-1)/3 (R1024 still has 4 k's remain)

sweety439 · 2018-01-07, 19:53

Quote:

Originally Posted by MisterBitcoin

I would be very happy if you would post an list with every PRP you found in your project. (sorted by base please)
I´m willing to test some of those PRP´s with primo, like I did on (6^1189*5741-1)/5, which is prime.

Also the (probable) prime (751*4^6615-1)/3, which is found by the Riesel 2nd conjecture base 4. (the CK's for R4: 1st is 361, 2nd is 919, 3rd is 1114, all of them are fully proven if the (probable) prime (751*4^6615-1)/3 is proven to be prime)

sweety439 · 2018-01-07, 22:04

This file is for the reversed Sierpinski/Riesel problems, i.e. find and prove the smallest base b>=2 such that (k*b^n+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime for all n>=1. (for 1<=k<=64)

Note: It can be shown that there is no base b such that 1 is Sierpinski number, and there is no base b such that 1, 2 or 3 is Riesel number. The smallest base b such that 2 is Sierpinski number is conjectured to be 201446503145165177 (see the project http://mersenneforum.org/showthread.php?t=21951) (2 is not Sierpinski number for all bases b congruent to 1 mod 3), and I am now searching the smallest base b such that 3 is Sierpinski number (it can be shown that all bases b such that 3 is Sierpinski number are congruent to 3 mod 4).

This file is for 1<=k<=64, totally 128 conjectures (include the conjecture that there is no base b such that 1 is Sierpinski number and there is no base b such that 1, 2 or 3 is Riesel number), most of these conjectures are proven, however, the conjectures of k = 1, 2 and 3 are very hard and will not be proven before 2200.

sweety439 · 2018-01-07, 22:13

Quote:

Originally Posted by sweety439

This file is for the reversed Sierpinski/Riesel problems, i.e. find and prove the smallest base b>=2 such that (k*b^n+-1)/gcd(k+-1,b-1) (+ for Sierpinski, - for Riesel) is not prime for all n>=1. (for 1<=k<=64)

Note: It can be shown that there is no base b such that 1 is Sierpinski number, and there is no base b such that 1, 2 or 3 is Riesel number. The smallest base b such that 2 is Sierpinski number is conjectured to be 201446503145165177 (see the project http://mersenneforum.org/showthread.php?t=21951), and I am now searching the smallest base b such that 3 is Sierpinski number (it can be shown that all bases b such that 3 is Sierpinski number are odd).

This base is 158503, update the file to include it. (only searched the primes p<=30000, and exponent n are only tested to n=2000)

The covering set of this base is {2, 5, 17, 41, 193}.

sweety439 · 2018-01-09, 22:12

Quote:

Originally Posted by sweety439

In fact,

All k = 7 or 11 mod 24 are Sierpinski in base 5. (with covering set {2, 3})
All k = 13 or 17 mod 24 are Riesel in base 5. (with covering set {2, 3})
All k = 47, 79, 83 or 181 mod 195 are Sierpinski in base 8. (with covering set {3, 5, 13})
All k = 14, 112, 116 or 148 mod 195 are Riesel in base 8. (with covering set {3, 5, 13})
All k = 31 or 39 mod 80 are Sierpinski in base 9. (with covering set {2, 5})
All k = 41 or 49 mod 80 are Riesel in base 9. (with covering set {2, 5})
All k = 5 or 7 mod 12 are both Sierpinski and Riesel in base 11. (with covering set {2, 3})
All k = 15 or 27 mod 56 are Sierpinski in base 13. (with covering set {2, 7})
All k = 29 or 41 mod 56 are Riesel in base 13. (with covering set {2, 7})
All k = 4 or 11 mod 15 are both Sierpinski and Riesel in base 14. (with covering set {3, 5})
All k = 31 or 47 mod 96 are Sierpinski in base 17. (with covering set {2, 3})
All k = 49 or 65 mod 96 are Riesel in base 17. (with covering set {2, 3})
All k = 9 or 11 mod 20 are both Sierpinski and Riesel in base 19. (with covering set {2, 5})
All k = 8 or 13 mod 21 are both Sierpinski and Riesel in base 20. (with covering set {3, 7})
All k = 23 or 43 mod 88 are Sierpinski in base 21. (with covering set {2, 11})
All k = 45 or 65 mod 88 are Riesel in base 21. (with covering set {2, 11})
All k = 5 or 7 mod 12 are both Sierpinski and Riesel in base 23. (with covering set {2, 3})
All k = 79 or 103 mod 208 are Sierpinski in base 25. (with covering set {2, 13})
All k = 105 or 129 mod 208 are Riesel in base 25. (with covering set {2, 13})
All k = 13 or 15 mod 28 are both Sierpinski and Riesel in base 27. (with covering set {2, 7})
All k = 4 or 11 mod 15 (with covering set {3, 5}) and all k = 7 or 11 mod 24 (with covering set {2, 3}) and all k = 19 or 31 mod 40 (with covering set {2, 5}) are Sierpinski in base 29.
All k = 4 or 11 mod 15 (with covering set {3, 5}) and all k = 13 or 17 mod 24 (with covering set {2, 3}) and all k = 9 or 21 mod 40 (with covering set {2, 5}) are Riesel in base 29.
All k = 10 or 23 mod 33 are both Sierpinski and Riesel in base 32. (with covering set {3, 11})

The smallest k != 7 or 11 mod 24 which is Sierpinski in base 5 is 159986. (with covering set {3, 7, 13, 31, 601})
The smallest k != 47, 79, 83 or 181 mod 195 which is Sierpinski in base 8 is 1175. (with covering set {3, 13, 17, 241})
The smallest k != 31 or 39 mod 80 which is Sierpinski in base 9 is 2344. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Sierpinski in base 11 is 369. (with covering set {2, 7, 19, 37})
The smallest k != 15 or 27 mod 56 which is Sierpinski in base 13 is 47. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is still finding...
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is still finding...
The smallest k != 14, 112, 116 or 148 mod 195 which is Riesel in base 8 is 658. (with covering set {3, 5, 19, 37, 73})
The smallest k != 41 or 49 mod 80 which is Riesel in base 9 is 74. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Riesel in base 11 is 862. (with covering set {3, 7, 19, 37})
The smallest k != 29 or 41 mod 56 which is Riesel in base 13 is 69. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is still finding...

sweety439 · 2018-01-09, 22:31

Quote:

Originally Posted by sweety439

The smallest k != 7 or 11 mod 24 which is Sierpinski in base 5 is 159986. (with covering set {3, 7, 13, 31, 601})
The smallest k != 47, 79, 83 or 181 mod 195 which is Sierpinski in base 8 is 1175. (with covering set {3, 13, 17, 241})
The smallest k != 31 or 39 mod 80 which is Sierpinski in base 9 is 2344. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Sierpinski in base 11 is 369. (with covering set {2, 7, 19, 37})
The smallest k != 15 or 27 mod 56 which is Sierpinski in base 13 is 47. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is still finding...
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is still finding...
The smallest k != 14, 112, 116 or 148 mod 195 which is Riesel in base 8 is 658. (with covering set {3, 5, 19, 37, 73})
The smallest k != 41 or 49 mod 80 which is Riesel in base 9 is 74. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Riesel in base 11 is 862. (with covering set {3, 7, 19, 37})
The smallest k != 29 or 41 mod 56 which is Riesel in base 13 is 69. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is still finding...

Update the files for the status for the Riesel side (except R5 and R14).

sweety439 · 2018-01-09, 22:54

Quote:

Originally Posted by sweety439

The smallest k != 7 or 11 mod 24 which is Sierpinski in base 5 is 159986. (with covering set {3, 7, 13, 31, 601})
The smallest k != 47, 79, 83 or 181 mod 195 which is Sierpinski in base 8 is 1175. (with covering set {3, 13, 17, 241})
The smallest k != 31 or 39 mod 80 which is Sierpinski in base 9 is 2344. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Sierpinski in base 11 is 369. (with covering set {2, 7, 19, 37})
The smallest k != 15 or 27 mod 56 which is Sierpinski in base 13 is 47. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is still finding...
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is still finding...
The smallest k != 14, 112, 116 or 148 mod 195 which is Riesel in base 8 is 658. (with covering set {3, 5, 19, 37, 73})
The smallest k != 41 or 49 mod 80 which is Riesel in base 9 is 74. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Riesel in base 11 is 862. (with covering set {3, 7, 19, 37})
The smallest k != 29 or 41 mod 56 which is Riesel in base 13 is 69. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is still finding...

Update the files for the status for the Sierpinski side (except S5 and S14).

sweety439 · 2018-01-09, 23:01

Quote:

Originally Posted by sweety439

The smallest k != 7 or 11 mod 24 which is Sierpinski in base 5 is 159986. (with covering set {3, 7, 13, 31, 601})
The smallest k != 47, 79, 83 or 181 mod 195 which is Sierpinski in base 8 is 1175. (with covering set {3, 13, 17, 241})
The smallest k != 31 or 39 mod 80 which is Sierpinski in base 9 is 2344. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Sierpinski in base 11 is 369. (with covering set {2, 7, 19, 37})
The smallest k != 15 or 27 mod 56 which is Sierpinski in base 13 is 47. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is still finding...
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is still finding...
The smallest k != 14, 112, 116 or 148 mod 195 which is Riesel in base 8 is 658. (with covering set {3, 5, 19, 37, 73})
The smallest k != 41 or 49 mod 80 which is Riesel in base 9 is 74. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Riesel in base 11 is 862. (with covering set {3, 7, 19, 37})
The smallest k != 29 or 41 mod 56 which is Riesel in base 13 is 69. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is still finding...

The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is 6647948.
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is 346802.
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is 2215067.

sweety439 · 2018-01-09, 23:06

Quote:

Originally Posted by sweety439

The smallest k != 7 or 11 mod 24 which is Sierpinski in base 5 is 159986. (with covering set {3, 7, 13, 31, 601})
The smallest k != 47, 79, 83 or 181 mod 195 which is Sierpinski in base 8 is 1175. (with covering set {3, 13, 17, 241})
The smallest k != 31 or 39 mod 80 which is Sierpinski in base 9 is 2344. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Sierpinski in base 11 is 369. (with covering set {2, 7, 19, 37})
The smallest k != 15 or 27 mod 56 which is Sierpinski in base 13 is 47. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Sierpinski in base 14 is still finding...
The smallest k != 13 or 17 mod 24 which is Riesel in base 5 is still finding...
The smallest k != 14, 112, 116 or 148 mod 195 which is Riesel in base 8 is 658. (with covering set {3, 5, 19, 37, 73})
The smallest k != 41 or 49 mod 80 which is Riesel in base 9 is 74. (with covering set {5, 7, 13, 73})
The smallest k != 5 or 7 mod 12 which is Riesel in base 11 is 862. (with covering set {3, 7, 19, 37})
The smallest k != 29 or 41 mod 56 which is Riesel in base 13 is 69. (with covering set {2, 5, 17})
The smallest k != 4 or 11 mod 15 which is Riesel in base 14 is still finding...

S8 has 4 k's remain: 256, 467, 1028, 1132.
S9 has 6 k's remain: 1039, 1627, 1801, 2007, 2036, 2287.
S11 has 2 k's remain: 195 and 237.
S13 has no k's remain.
R8 has 2 k's remain: 239 and 247.
R9 has no k's remain.
R11 has 5 k's remain: 201, 243, 851, 855, 856.
R13 has no k's remain.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
The dual Sierpinski/Riesel problem	sweety439	sweety439	14	2021-02-15 15:58
Semiprime and n-almost prime candidate for the k's with algebra for the Sierpinski/Riesel problem	sweety439	sweety439	11	2020-09-23 01:42
The reverse Sierpinski/Riesel problem	sweety439	sweety439	20	2020-07-03 17:22
Sierpinski/ Riesel bases 6 to 18	robert44444uk	Conjectures 'R Us	139	2007-12-17 05:17
Sierpinski/Riesel Base 10	rogue	Conjectures 'R Us	11	2007-12-17 05:08

2018-01-06, 15:05	#551
MisterBitcoin "Nuri, the dragon :P" Jul 2016 Good old Germany 3·271 Posts	I would be very happy if you would post an list with every PRP you found in your project. (sorted by base please) I´m willing to test some of those PRP´s with primo, like I did on (6^1189*5741-1)/5, which is prime.