mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > sweety439

Reply
 
Thread Tools
Old 2020-10-19, 15:47   #1068
sweety439
 
sweety439's Avatar
 
Nov 2016

248610 Posts
Default

At n=26544, found a new (probable) prime: (376*70^24952-1)/3
Attached Files
File Type: log pfgw.log (100 Bytes, 9 views)
sweety439 is online now   Reply With Quote
Old 2020-10-22, 14:48   #1069
sweety439
 
sweety439's Avatar
 
Nov 2016

46668 Posts
Default

For the Sierpinski bases 2<=b<=128 and b = 256, 512, 1024:

proven: 4, 5, 7, 8, 9, 11, 13, 14, 16, 17, 19, 20, 21, 23, 27, 29, 34, 35, 39, 41, 43, 44, 45, 47, 49, 51, 54, 56, 57, 59, 61, 64, 65, 69, 71, 73 (with PRP), 74, 75, 76, 79, 84, 85, 87, 88, 90, 94, 95, 100, 101, 105 (with PRP), 110, 111, 114, 116, 119, 121, 125, 256 (with PRP)
weak proven (only GFN's or half GFN's remain): 12, 18, 32, 37, 38, 50, 55, 62, 72, 77, 89, 91, 92, 98, 99, 104, 107, 109
1k bases: 25, 53, 103, 113, 118
2k bases but become 1k bases if GFN's and half GFN's are excluded: 10, 36, 68, 83, 86, 117, 122, 128
4k bases but become 1k bases if GFN's and half GFN's are excluded: 512
2k bases: 26, 30, 33, 46, 115
3k bases but become 2k bases if GFN's and half GFN's are excluded: 67, 123
3k bases: 28, 102
4k bases but become 3k bases if GFN's and half GFN's are excluded: 93
5k bases but become 3k bases if GFN's and half GFN's are excluded: 1024
sweety439 is online now   Reply With Quote
Old 2020-10-22, 14:59   #1070
sweety439
 
sweety439's Avatar
 
Nov 2016

46668 Posts
Default

For the Riesel bases 2<=b<=128 and b = 256, 512, 1024:

proven: 4, 5, 7 (with PRP), 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 25, 26, 27, 29, 32, 34, 35, 37, 38, 39, 41, 44, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 62, 64, 65, 67, 68, 69, 71, 72, 73 (with PRP), 74, 75, 76, 77, 79, 81, 83, 84, 86, 87, 89, 90, 91 (with PRP), 92, 95, 98, 99, 100 (with PRP), 101, 103, 104, 107 (with PRP), 109, 110, 111, 113, 114, 116, 119, 121, 122, 125, 128, 256, 512
1k bases: 43, 70, 85, 94, 97, 118, 123
2k bases: 33, 105, 115
3k bases: 46, 61, 80
sweety439 is online now   Reply With Quote
Old 2020-10-25, 19:43   #1071
sweety439
 
sweety439's Avatar
 
Nov 2016

46668 Posts
Default

Quote:
Originally Posted by sweety439 View Post
No other (probable) primes found for R70 k = 376, 496, 811 up to n=22813
R70 at n=37634, no new (probable) prime found
sweety439 is online now   Reply With Quote
Old 2020-10-28, 00:07   #1072
sweety439
 
sweety439's Avatar
 
Nov 2016

2×11×113 Posts
Default

R70 at n=41326, no other (probable) primes found
Attached Files
File Type: txt R70 status.txt (73.3 KB, 5 views)
sweety439 is online now   Reply With Quote
Old 2020-10-28, 00:09   #1073
sweety439
 
sweety439's Avatar
 
Nov 2016

9B616 Posts
Default

R43 at n=18122, no (probable) primes found

Unfortunately, srsieve cannot sieve R43, since k and b are both odd.
Attached Files
File Type: txt R43 status.txt (618.6 KB, 5 views)
sweety439 is online now   Reply With Quote
Old 2020-10-29, 00:49   #1074
sweety439
 
sweety439's Avatar
 
Nov 2016

2×11×113 Posts
Default

Quote:
Originally Posted by sweety439 View Post
R70 at n=41326, no other (probable) primes found
R70 at n=43008, one new (probable) prime found: (376*70^42427-1)/3

Unfortunately, this does not help for the R70 problem, since k=376 already has the prime (376*70^6484-1)/3, and the only remain k (k=811) still does not have any (probable) primes

Last fiddled with by sweety439 on 2020-10-29 at 00:50
sweety439 is online now   Reply With Quote
Old 2020-10-29, 03:28   #1075
sweety439
 
sweety439's Avatar
 
Nov 2016

2×11×113 Posts
Default

If k is rational power of base (b), then .... (let k = b^(r/s) with gcd(r,s) = 1)

* For the Riesel case, this is generalized repunit number to base b^(1/s)
* For the Sierpinski case, if s is odd, then this is generalized (half) Fermat number to base b^(1/s)
* For the Sierpinski case, if s is even, then this is generalized repunit number to negative base -b^(1/s)
sweety439 is online now   Reply With Quote
Old 2020-10-31, 00:22   #1076
sweety439
 
sweety439's Avatar
 
Nov 2016

46668 Posts
Default

These problems generalized the Sierpinski problem and the Riesel problem to other bases (instead of only base 2), since for bases b>2, k*b^n+1 is always divisible by gcd(k+1,b-1) and k*b^n-1 is always divisible by gcd(k-1,b-1), the formulas are (k*b^n+1)/gcd(k+1,b-1) for Sierpinski and (k*b^n-1)/gcd(k-1,b-1) for Riesel, for a given base b>=2, we will find and proof the smallest k>=1 such that (k*b^n+1)/gcd(k+1,b-1) (for Sierpinski) or (k*b^n-1)/gcd(k-1,b-1) (for Riesel) is not prime for all n>=1, any k that obtains a full covering set in any manner from ALGEBRAIC factors will be excluded, in many instances, this includes k's where there is a partial covering set of numeric factors (or a single numeric factor) and a partial covering set of algebraic factors that combine to make a full covering set, all k below the lowest k found to have a NUMERIC covering set must have a prime including multiples of the base (MOB) but excluding the k's that obtains a full covering set in any manner from ALGEBRAIC factors, for the lowest k found to have a NUMERIC covering set for all bases b<=2048 and b = 4096, 8192, 16384, 32768, 65536, see Sierpinski and Riesel
sweety439 is online now   Reply With Quote
Old 2020-10-31, 00:24   #1077
sweety439
 
sweety439's Avatar
 
Nov 2016

2×11×113 Posts
Default

reserving S36 k=1814 for n = 87.5K - 100K, currently at n=92334, no (probable) prime found
Attached Files
File Type: txt S36 status.txt (19.6 KB, 5 views)
sweety439 is online now   Reply With Quote
Old 2020-10-31, 00:54   #1078
sweety439
 
sweety439's Avatar
 
Nov 2016

2×11×113 Posts
Default

For Riesel problem base b, k=1 proven composite by algebra factors if and only if b is perfect power (of the form m^r with r>1)

For Sierpinski problem base b, k=1 proven composite by algebra factors if and only if b is perfect odd power (of the form m^r with odd r>1)

In Riesel problem base b, k=1 can only have prime for n which is prime

In Sierpinski problem base b, k=1 can only have prime for n which is power of 2
sweety439 is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
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
The dual Sierpinski/Riesel problem sweety439 sweety439 12 2017-12-01 21:56
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

All times are UTC. The time now is 04:29.

Thu Nov 26 04:29:06 UTC 2020 up 77 days, 1:40, 4 users, load averages: 1.62, 1.82, 1.82

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.