(81853673 - 1)/8184
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: | (81853673 - 1)/8184 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized repunit |
| Proof-code(s): (*): | x14 : Steward, OpenPFGW, Primo |
| Decimal Digits: | 14369 (log10 is 14368.604659786) |
| Rank (*): | 80893 (digit rank is 1) |
| Entrance Rank (*): | 16083 |
| Currently on list? (*): | no |
| Submitted: | 7/7/2003 21:49:24 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 65437 |
| Status Flags: | Verify |
| Score (*): | 33.5629 (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.
- Generalized Repunit (archivable *)
- Prime on list: no, rank 65
Subcategory: "Generalized Repunit"
(archival tag id 192578, tag last modified 2025-09-11 16:37:14)
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 65437 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 11 Primality testing (8185^3673-1)/8184 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N+1 test using discriminant 43, base 12+sqrt(43) Calling N-1 BLS with factored part 1.15% and helper 0.01% (3.46% proof) (8185^3673-1)/8184 is Fermat and Lucas PRP! (262.160000 seconds) modified 2020-07-07 22:30:47 created 2003-07-11 13:54:47 id 70312
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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