primU(43121)
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: | primU(43121) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Fibonacci primitive part, ECPP |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 7975 (log10 is 7974.8278561772) |
| Rank (*): | 84958 (digit rank is 1) |
| Entrance Rank (*): | 66612 |
| Currently on list? (*): | short |
| Submitted: | 8/14/2013 14:40:37 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 115080 |
| Status Flags: | Verify |
| Score (*): | 31.7384 (normalized score 0) |
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 400
Subcategory: "ECPP"
(archival tag id 217206, tag last modified 2024-04-13 23:37:20)- Fibonacci Primitive Part (archivable *)
- Prime on list: yes, rank 18
Subcategory: "Fibonacci Primitive Part"
(archival tag id 217207, 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 115080 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 6727538274060043....6229669906411201 1/1 mro=0 trial factoring to 2249451 6727538274...9906411201 has no small factor. [Elapsed time: 119.487 seconds] modified 2020-07-07 22:30:18 created 2013-08-14 14:42:32 id 160534
field value prime_id 115080 person_id 9 machine WinXP Dual Core 2.6GHz 64-bit Laptop what prp notes Command: pfgw64.exe -tc p_115080.txt 2>&1 PFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing 6727538274...9906411201 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 37 Running N-1 test using base 43 Running N+1 test using discriminant 67, base 14+sqrt(67) Calling N-1 BLS with factored part 0.53% and helper 0.00% (1.59% proof) 6727538274...9906411201 is Fermat and Lucas PRP! (7.0461s+0.0049s) [Elapsed time: 7 seconds] modified 2020-07-07 22:30:18 created 2013-08-14 15:36:49 id 160545
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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