20180503, 21:29  #1 
Nov 2016
2^{2}×3×179 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. Last fiddled with by sweety439 on 20180503 at 21:30 
20180506, 02:12  #4 
Jun 2003
2×3^{3}×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. 
20190207, 00:48  #5 
Sep 2003
101000010011_{2} Posts 
From OEIS A028491, Paul Bourdelais has discovered a new base3 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 20190207 at 00:58 
20190207, 13:25  #6  
Jun 2015
Vallejo, CA/.
7·137 Posts 
Quote:


20191114, 13:21  #7 
Jul 2003
584_{10} Posts 
hi,
reserving R[6] from n=608100 to 1000000 
20191214, 10:19  #8 
Jul 2003
2^{3}·73 Posts 

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