p(50001890)
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: | p(50001890) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c46 : Boncompagni, Primo |
| Decimal Digits: | 7869 (log10 is 7868.839822877) |
| Rank (*): | 85032 (digit rank is 1) |
| Entrance Rank (*): | 56388 |
| Currently on list? (*): | no |
| Submitted: | 8/31/2011 22:02:57 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 101406 |
| Blob database id: | 267 |
| Status Flags: | Verify |
| Score (*): | 31.6969 (normalized score 0) |
Description: (from blob table id=267)
p(50001890) is the number of partitions of the number\r\n50001890. For the primality proof, see the PRIMO certificate.
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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 403
Subcategory: "ECPP"
(archival tag id 213405, tag last modified 2024-04-13 23:37:20)- Partitions (archivable *)
- Prime on list: no, rank 69
Subcategory: "Partitions"
(archival tag id 213406, tag last modified 2023-03-11 15:53:59)
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 101406 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 6915055197512934....7376211670756619 1/1 mro=0 trial factoring to 2217114 6915055197...1670756619 has no small factor. [Elapsed time: 8.000 seconds] modified 2020-07-07 22:30:31 created 2011-08-31 22:05:02 id 132374
field value prime_id 101406 person_id 9 machine RedHat Virtual STEM Server what prp notes PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 6915055197...1670756619 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N+1 BLS with factored part 0.07% and helper 0.03% (0.25% proof) 6915055197...1670756619 is Fermat and Lucas PRP! (11.4651s+0.0090s) [Elapsed time: 11.00 seconds] modified 2020-07-07 22:30:31 created 2011-08-31 23:10:09 id 132389
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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