(210007 - 1)/20453755399107134938775648992529401
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: | (210007 - 1)/20453755399107134938775648992529401 |
---|---|
Verification status (*): | PRP |
Official Comment (*): | Mersenne cofactor, ECPP |
Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
Decimal Digits: | 2979 (log10 is 2978.0963935514) |
Rank (*): | 96589 (digit rank is 2) |
Entrance Rank (*): | 28246 |
Currently on list? (*): | no |
Submitted: | 6/27/2002 16:03:49 UTC |
Last modified: | 3/11/2023 15:54:10 UTC |
Database id: | 29753 |
Status Flags: | Verify |
Score (*): | 28.6777 (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 43
Subcategory: "Mersenne cofactor"
(archival tag id 175452, tag last modified 2024-04-11 03:37:12)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 762
Subcategory: "ECPP"
(archival tag id 175451, tag last modified 2024-04-19 02:37:11)
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 29753 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 3 Primality testing (2^10007-1)/(14477908246561*136255313*10368448917257) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 8+sqrt(7) Calling N-1 BLS with factored part 0.54% and helper 0.35% (1.97% proof) (2^10007-1)/(14477908246561*136255313*10368448917257) is Fermat and Lucas PRP! (113.130000 seconds) modified 2003-03-25 17:22:58 created 2003-01-04 21:28:29 id 61854
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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