(219121 - 1)/917809 / 415147656569 / 1531543915081 / 27784129616513881634842031
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: | (219121 - 1)/917809 / 415147656569 / 1531543915081 / 27784129616513881634842031 |
|---|---|
| Verification status (*): | External |
| Official Comment (*): | Mersenne cofactor |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c78 : Alpern, Sorbera, Primo |
| Decimal Digits: | 5701 (log10 is 5700.7846659377) |
| Rank (*): | 89532 (digit rank is 2) |
| Entrance Rank (*): | 74941 |
| Currently on list? (*): | no |
| Submitted: | 4/13/2015 20:08:46 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 119721 |
| Status Flags: | Verify |
| Score (*): | 30.6966 (normalized score 0) |
Archival tags:
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.
- Mersenne cofactor (archivable *)
- Prime on list: no, rank 32
Subcategory: "Mersenne cofactor"
(archival tag id 219099, tag last modified 2024-04-11 03:37:12)
User comments about this prime (disclaimer):
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Verification data:
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 119721 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^19121-1)/917809/415147656569/1531543915081/27784129616513881634842031" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (2^19121-1)/917809/415147656569/1531543915081/2778412961...1634842031 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 0.35% and helper 0.10% (1.17% proof) (2^19121-1)/917809/415147656569/1531543915081/2778412961...1634842031 is Fermat and Lucas PRP! (2.3167s+0.0003s) [Elapsed time: 2.00 seconds] modified 2020-07-07 22:30:17 created 2015-04-13 20:11:01 id 165335
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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