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sweety439 2018-05-03 21:29

Generalized repunit (probable) prime search
 
2 Attachment(s)
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.

JeppeSN 2018-05-05 23:29

You could submit this information to the OEIS entries which are [URL="https://oeis.org/A128164"]A128164[/URL] and [URL="https://oeis.org/A084742"]A084742[/URL], respectively. /JeppeSN

sweety439 2018-05-06 01:28

[QUOTE=JeppeSN;487051]You could submit this information to the OEIS entries which are [URL="https://oeis.org/A128164"]A128164[/URL] and [URL="https://oeis.org/A084742"]A084742[/URL], respectively. /JeppeSN[/QUOTE]

I do not have OEIS account and not decide to create.

Citrix 2018-05-06 02:12

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.

GP2 2019-02-07 00:48

From [URL="http://oeis.org/A028491"]OEIS A028491[/URL], Paul Bourdelais has discovered a new base-3 repunit (probable) prime:

(3^2215303 − 1) /2 is a PRP


The [URL="http://www.primenumbers.net/prptop/prptop.php"]Lifchitz PRP Top page[/URL] shows two other discoveries in January for bases −6 and −7:

(6^1313371 + 1) /7
(7^1178033 + 1) /8

rudy235 2019-02-07 13:25

[QUOTE=GP2;507879]From [URL="http://oeis.org/A028491"]OEIS A028491[/URL], Paul Bourdelais has discovered a new base-3 repunit (probable) prime:

(3^2215303 − 1) /2 is a PRP[/quote] [COLOR="Red"]1'057,967 digits
[/COLOR]

lalera 2019-11-14 13:21

hi,
reserving R[6]
from n=608100 to 1000000

lalera 2019-12-14 10:19

[QUOTE=lalera;530558]hi,
reserving R[6]
from n=608100 to 1000000[/QUOTE]

range done. no prp found


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