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(2106391 - 1)/286105171290931103
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
|Description:||(2106391 - 1)/286105171290931103|
|Verification status (*):||PRP|
|Official Comment (*):||Mersenne cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c95 : Gelhar, Primo|
|Decimal Digits:||32010 (log10 is 32009.425742979)|
|Rank (*):||65715 (digit rank is 1)|
|Entrance Rank (*):||63854|
|Currently on list? (*):||short|
|Submitted:||4/27/2022 23:07:49 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Status Flags:||Verify, TrialDiv|
|Score (*):||36.04 (normalized score 0.0001)|
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 21
(archival tag id 227023, tag last modified 2023-03-11 16:02:30)
- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 3
Subcategory: "Mersenne cofactor"
(archival tag id 227024, tag last modified 2023-03-11 16:02:31)
User comments about this prime (disclaimer):
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The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
field value prime_id 133882 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^106391-1)/286105171290931103" 2>&1 PFGW Version 184.108.40.206BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (2^106391-1)/286105171290931103 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 29, base 14+sqrt(29) Calling N-1 BLS with factored part 0.04% and helper 0.01% (0.14% proof) (2^106391-1)/286105171290931103 is Fermat and Lucas PRP! (31.2094s+0.0001s) [Elapsed time: 31.00 seconds] modified 2022-07-11 18:21:44 created 2022-04-27 23:11:01 id 179604
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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