p(7512392)
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(7512392) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c42 : Peets, Primo |
| Decimal Digits: | 3046 (log10 is 3045.6412341826) |
| Rank (*): | 95894 (digit rank is 1) |
| Entrance Rank (*): | 45748 |
| Currently on list? (*): | no |
| Submitted: | 4/21/2007 11:47:35 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 80113 |
| Blob database id: | 204 |
| Status Flags: | Verify |
| Score (*): | 28.7475 (normalized score 0) |
Description: (from blob table id=204)
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 735
Subcategory: "ECPP"
(archival tag id 185647, tag last modified 2024-04-24 05:37:26)- Partitions (archivable *)
- Prime on list: no, rank 115
Subcategory: "Partitions"
(archival tag id 185648, 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 80113 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 4376872958...3619074154.........1738212273716034 1/1 trial factoring to 790910 4376872958...4571706531 has no small factor. [Elapsed time: 1.265 seconds] modified 2020-07-07 22:30:41 created 2007-04-21 11:52:02 id 89335
field value prime_id 80113 person_id 9 machine RedHat P4 P4 what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4376872958...4571706531 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 20244 bit request FFT size=(1280,16) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1280,22) to FFT(1280,21) Reduced from FFT(1280,21) to FFT(1280,20) Reduced from FFT(1280,20) to FFT(1280,19) Reduced from FFT(1280,19) to FFT(1280,18) Reduced from FFT(1280,18) to FFT(1280,17) Reduced from FFT(1280,17) to FFT(1280,16) 20252 bit request FFT size=(1280,16) Calling N-1 BLS with factored part 0.22% and helper 0.11% (0.76% proof) 4376872958...4571706531 is Fermat and Lucas PRP! (3.7200s+0.0000s) [Elapsed time: 4 seconds] modified 2020-07-07 22:30:41 created 2007-04-21 11:53:01 id 89336
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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