(263703 - 1)/42808417
|Description:||(263703 - 1)/42808417|
|Verification status (*):||PRP|
|Official Comment (*):||Mersenne cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c59 : Metcalfe, OpenPFGW, Primo|
|Decimal Digits:||19169 (log10 is 19168.882284614)|
|Rank (*):||69420 (digit rank is 1)|
|Entrance Rank (*):||58136|
|Currently on list? (*):||short|
|Submitted:||1/9/2014 13:21:24 CDT|
|Last modified:||1/9/2014 13:51:04 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||34.455 (normalized score 0)|
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 41
(archival tag id 217568, tag last modified 2021-09-18 09:37:41)
- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 3
Subcategory: "Mersenne cofactor"
(archival tag id 217569, tag last modified 2021-02-24 00:50:28)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 116871 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(2^63703-1)/42808417" 2>&1 PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (2^63703-1)/42808417 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N-1 BLS with factored part 0.12% and helper 0.01% (0.36% proof) (2^63703-1)/42808417 is Fermat and Lucas PRP! (233.6976s+0.0004s) [Elapsed time: 3.90 minutes] modified 2020-07-07 17:30:18 created 2014-01-09 13:23:01 id 162380
Query times: 0.0002 seconds to select prime, 0.0028 seconds to seek comments.
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