p(23028252)
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(23028252) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c42 : Peets, Primo |
| Decimal Digits: | 5338 (log10 is 5337.6750909744) |
| Rank (*): | 90505 (digit rank is 5) |
| Entrance Rank (*): | 46064 |
| Currently on list? (*): | no |
| Submitted: | 12/1/2008 23:48:48 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 85862 |
| Blob database id: | 218 |
| Status Flags: | Verify |
| Score (*): | 30.4922 (normalized score 0) |
Description: (from blob table id=218)
[This prime has a pre-calculated decimal expansion (linked blob)]
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.
- Partitions (archivable *)
- Prime on list: no, rank 88
Subcategory: "Partitions"
(archival tag id 195037, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 536
Subcategory: "ECPP"
(archival tag id 195036, tag last modified 2024-04-24 05:37:26)
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 85862 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 4732066679...7038739927.........1841092908313890 1/1 trial factoring to 1455778 4732066679...0147810421 has no small factor. [Elapsed time: 2.960 seconds] modified 2020-07-07 22:30:39 created 2008-12-01 23:52:01 id 101192
field value prime_id 85862 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 4732066679...0147810421 [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(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) 35472 bit request FFT size=(2048,18) Running N+1 test using discriminant 7, base 1+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2048,21) to FFT(2048,20) Reduced from FFT(2048,20) to FFT(2048,19) Reduced from FFT(2048,19) to FFT(2048,18) 35480 bit request FFT size=(2048,18) Calling N-1 BLS with factored part 0.14% and helper 0.14% (0.57% proof) 4732066679...0147810421 is Fermat and Lucas PRP! (10.0800s+0.0000s) [Elapsed time: 11.00 seconds] modified 2020-07-07 22:30:39 created 2008-12-01 23:53:02 id 101193
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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