p(11005236)
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(11005236) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c42 : Peets, Primo |
| Decimal Digits: | 3688 (log10 is 3687.7456579073) |
| Rank (*): | 94209 (digit rank is 5) |
| Entrance Rank (*): | 44241 |
| Currently on list? (*): | no |
| Submitted: | 4/26/2007 23:38:50 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 80220 |
| Blob database id: | 206 |
| Status Flags: | Verify |
| Score (*): | 29.3428 (normalized score 0) |
Description: (from blob table id=206)
[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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 674
Subcategory: "ECPP"
(archival tag id 185674, tag last modified 2024-04-24 05:37:26)- Partitions (archivable *)
- Prime on list: no, rank 113
Subcategory: "Partitions"
(archival tag id 185675, 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 80220 person_id 9 machine RedHat P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 5566726360...0569800862.........1097098833312724 1/1 trial factoring to 974063 5566726360...4567520887 has no small factor. [Elapsed time: 1.848 seconds] modified 2020-07-07 22:30:41 created 2007-04-26 23:52:02 id 89551
field value prime_id 80220 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 5566726360...4567520887 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24510 bit request FFT size=(1536,17) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24518 bit request FFT size=(1536,17) Calling N+1 BLS with factored part 0.03% and helper 0.01% (0.11% proof) 5566726360...4567520887 is Fermat and Lucas PRP! (5.3600s+0.0000s) [Elapsed time: 5 seconds] modified 2020-07-07 22:30:41 created 2007-04-26 23:53:01 id 89552
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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