E(1840)/31237282053878368942060412182384934425
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: | E(1840)/31237282053878368942060412182384934425 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Euler irregular, ECPP |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 4812 (log10 is 4811.9441292945) |
| Rank (*): | 93049 (digit rank is 1) |
| Entrance Rank (*): | 61683 |
| Currently on list? (*): | yes |
| Submitted: | 5/17/2011 08:52:34 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 100107 |
| Blob database id: | 263 |
| Status Flags: | Verify |
| Score (*): | 30.17 (normalized score 0) |
Description: (from blob table id=263)
E(1840)/31237282053878368942060412182384934425
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.
- Euler Irregular primes (archivable *)
- Prime on list: yes, rank 14
Subcategory: "Euler Irregular primes"
(archival tag id 213232, tag last modified 2023-10-06 17:37:13)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 599
Subcategory: "ECPP"
(archival tag id 213233, tag last modified 2024-10-27 10:37:10)
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 100107 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 8792842510037036....0551156340736921 1/1 mro=0 trial factoring to 1300739 8792842510...6340736921 has no small factor. [Elapsed time: 3.007 seconds] modified 2020-07-07 22:30:31 created 2011-05-17 13:18:02 id 129788
field value prime_id 100107 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 8792842510...6340736921 [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 discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.09% and helper 0.03% (0.30% proof) 8792842510...6340736921 is Fermat and Lucas PRP! (8.2851s+0.0014s) [Elapsed time: 9.00 seconds] modified 2020-07-07 22:30:31 created 2011-05-17 13:30:15 id 129789
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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