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2018-05-03, 21:29   #1
sweety439

Nov 2016

2×23×47 Posts
Generalized repunit (probable) prime search

This thread is for finding the smallest generalized repunit (probable) prime for a fixed base b, I have searched them for all bases 2<=b<=1024 and -1024<=b<=-2, see the text files. Of course, I know that there is no generalized repunit prime in base b for some bases because of the algebra factors, all such bases are either perfect powers or of the form -4k^4. Besides, I have completed these ranges:

Positive bases:

b<=400 to n=50000.
401<=b<=512 to n=30000.
513<=b<=1024 to n=10000.

Negative bases:

b>=-400 to n=50000.
-512<=b<=-401 to n=30000.
-1024<=b<=-513 to n=8000.

Also, I extended these searches for some smaller base b with no (probable) prime found, for positive bases, I completed b=185 to n=66337, b=269 to n=63659 and b=281 to n=63421, and for negative bases, I completed b=-97 to n=59863, b=-103 to n=59509 and b=-113 to n=59021, all have still no (probable) prime found.
Attached Files
 smallest odd prime p such that (b^p-1)(b-1) is prime.txt (8.5 KB, 114 views) smallest odd prime p such that (b^p+1)(b+1) is prime.txt (8.7 KB, 119 views)

Last fiddled with by sweety439 on 2018-05-03 at 21:30

 2018-05-05, 23:29 #2 JeppeSN     "Jeppe" Jan 2016 Denmark 14210 Posts You could submit this information to the OEIS entries which are A128164 and A084742, respectively. /JeppeSN
2018-05-06, 01:28   #3
sweety439

Nov 2016

216210 Posts

Quote:
 Originally Posted by JeppeSN You could submit this information to the OEIS entries which are A128164 and A084742, respectively. /JeppeSN
I do not have OEIS account and not decide to create.

 2018-05-06, 02:12 #4 Citrix     Jun 2003 2×33×29 Posts How did you extend these ranges? Is there a good sieve software and fast PRP software. If you used PFGW - what setting did you use? Thanks.
 2019-02-07, 00:48 #5 GP2     Sep 2003 2,579 Posts From OEIS A028491, Paul Bourdelais has discovered a new base-3 repunit (probable) prime: (3^2215303 − 1) /2 is a PRP The Lifchitz PRP Top page shows two other discoveries in January for bases −6 and −7: (6^1313371 + 1) /7 (7^1178033 + 1) /8 Last fiddled with by GP2 on 2019-02-07 at 00:58
2019-02-07, 13:25   #6
rudy235

Jun 2015
Vallejo, CA/.

7·137 Posts

Quote:
 Originally Posted by GP2 From OEIS A028491, Paul Bourdelais has discovered a new base-3 repunit (probable) prime: (3^2215303 − 1) /2 is a PRP
1'057,967 digits

 2019-11-14, 13:21 #7 lalera     Jul 2003 23×73 Posts hi, reserving R[6] from n=608100 to 1000000
2019-12-14, 10:19   #8
lalera

Jul 2003

11108 Posts

Quote:
 Originally Posted by lalera hi, reserving R[6] from n=608100 to 1000000
range done. no prp found

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