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Old 2018-05-03, 21:29   #1
sweety439
 
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Default 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 2018-05-03 at 21:30
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Old 2018-05-05, 23:29   #2
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You could submit this information to the OEIS entries which are A128164 and A084742, respectively. /JeppeSN
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Old 2018-05-06, 01:28   #3
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Quote:
Originally Posted by JeppeSN View Post
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.
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Old 2018-05-06, 02:12   #4
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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.
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Old 2019-02-07, 00:48   #5
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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
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Old 2019-02-07, 13:25   #6
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Quote:
Originally Posted by GP2 View Post
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
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Old 2019-11-14, 13:21   #7
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hi,
reserving R[6]
from n=608100 to 1000000
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Old 2019-12-14, 10:19   #8
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Quote:
Originally Posted by lalera View Post
hi,
reserving R[6]
from n=608100 to 1000000
range done. no prp found
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