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Old 2021-06-22, 06:35   #1244
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22·3·7·37 Posts
Default

S40 completed to n=5000

Code:
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Old 2021-06-27, 12:47   #1245
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22·3·7·37 Posts
Default

Quote:
Originally Posted by sweety439 View Post
All remain k for R40 are searched to n=5000
Quote:
Originally Posted by sweety439 View Post
S40 completed to n=5000
Riesel problems and Sierpinski problems files updated.
Attached Files
File Type: pdf Riesel problems.pdf (381.6 KB, 56 views)
File Type: pdf Sierpinski problems.pdf (364.9 KB, 54 views)

Last fiddled with by sweety439 on 2021-07-30 at 06:36
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Old 2021-09-03, 23:28   #1247
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22×3×7×37 Posts
Default

Status for 2<=b<=128 and 1<=k<=128:

Sierpinski (k*b^n+1)/gcd(k+1,b-1)

Riesel (k*b^n-1)/gcd(k-1,b-1)
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Old 2021-09-03, 23:36   #1248
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22×3×7×37 Posts
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Word files attached.
Attached Files
File Type: zip Sierpinski and Riesel problems.zip (240.7 KB, 37 views)
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Old 2021-09-23, 07:58   #1249
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22×3×7×37 Posts
Default

The CK for bases b<=2500 and b=2^r with r<=16: Riesel Sierpinski

search limit: 10^9 for bases b<=1024, 5*10^6 for bases b>1024 (except R1216, the CK was searched and found since the CK for S1216 is < 5*10^6)

Note: I only searched with the primes <= 50000 (i.e. only remove (k*b^n+-1)/gcd(k+-1,b-1) with a prime factor <= 50000), and only searched (k*b^n+-1)/gcd(k+-1,b-1) for 1<=n<=3000

see posts in pages 92 and 93 and 94 for more information (when the CK > 5*10^6 for bases b<=1024 were being searched)

Last fiddled with by sweety439 on 2021-10-21 at 09:46
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Old 2021-09-23, 08:02   #1250
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22·3·7·37 Posts
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Formulas:

CRUS Riesel problems: k*b^n-1
Riesel problems in this project: (k*b^n-1)/gcd(k-1,b-1)
CRUS Sierpinski problems: k*b^n+1
Sierpinski problems in this project: (k*b^n+1)/gcd(k+1,b-1)
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Old 2021-10-01, 12:53   #1251
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

C2416 Posts
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Quote:
Originally Posted by rogue View Post
64*425^467857-1 is prime. This prime clocks in at 1229712 digits and proves R425. Woohoo!!!
The top proven conjectures are all related to perfect powers (i.e. either k or b is perfect power):

R72: 4*72^1119849-1, 4 is perfect power (2^2)
R121: 2622*121^810960-1, 121 is perfect power (11^2)
R100: 653*100^717513-1, 100 is perfect power (10^2)
R650: 4*650^498101-1, 4 is perfect power (2^2)
R425: 64*425^467857-1, 64 is perfect power (2^6)

S470: 32*470^683151+1, 32 is perfect power (2^5)
S676: 607*676^544517+1, 676 is perfect power (26^2)
S406: 100*406^543228+1, 100 is perfect power (10^2)
S797: 4*797^468702+1, 4 is perfect power (2^2)

is there any justification? (I know that, perfect power - 1, or perfect odd power + 1, or 4m^4+1, have algebraic factorization, maybe this is the reason ....)

MODERATOR NOTE: Post moved from "Bases 251-500 reservations/statuses/primes" thread as off-topic.

Last fiddled with by Dr Sardonicus on 2021-10-01 at 14:52
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