(228759 - 1)/226160777
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: | (228759 - 1)/226160777 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Mersenne cofactor, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c60 : Lemsafer, Primo |
| Decimal Digits: | 8649 (log10 is 8648.9672280129) |
| Rank (*): | 84130 (digit rank is 1) |
| Entrance Rank (*): | 62604 |
| Currently on list? (*): | no |
| Submitted: | 9/24/2012 15:40:16 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 109394 |
| Status Flags: | Verify |
| Score (*): | 31.9901 (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 364
Subcategory: "ECPP"
(archival tag id 214529, tag last modified 2024-04-13 23:37:20)- Mersenne cofactor (archivable *)
- Prime on list: no, rank 25
Subcategory: "Mersenne cofactor"
(archival tag id 214530, tag last modified 2024-04-11 03:37:12)
User comments about this prime (disclaimer):
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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 109394 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(2^28759-1)/226160777" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (2^28759-1)/226160777 1/1 mro=0 trial factoring to 2455982 (2^28759-1)/226160777 has no small factor. [Elapsed time: 1.976 seconds] modified 2020-07-07 22:30:24 created 2012-09-24 15:48:01 id 148434
field value prime_id 109394 person_id 9 machine RedHat Virtual STEM Server what prp notes Command: /home/caldwell/client/pfgw -tc -q"(2^28759-1)/226160777" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing (2^28759-1)/226160777 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N+1 BLS with factored part 0.09% and helper 0.08% (0.37% proof) (2^28759-1)/226160777 is Fermat and Lucas PRP! (23.8864s+0.0265s) [Elapsed time: 24.00 seconds] modified 2020-07-07 22:30:24 created 2012-09-24 15:52:49 id 148435
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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