192335307 · 225000 + 5129
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: | 192335307 · 225000 + 5129 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP, consecutive primes arithmetic progression (3,d=5130) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 7535 (log10 is 7534.0339506145) |
| Rank (*): | 88091 (digit rank is 25) |
| Entrance Rank (*): | 67587 |
| Currently on list? (*): | no |
| Submitted: | 9/4/2013 23:11:44 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 115384 |
| Status Flags: | Verify |
| Score (*): | 31.562 (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.
- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 17
Subcategory: "3/3"
(archival tag id 238618, tag last modified 2025-02-16 14:52:00)- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 129, weight 36.99689015139
Subcategory: "3/3"
(archival tag id 230358, tag last modified 2025-02-16 14:52:00)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 445
Subcategory: "ECPP"
(archival tag id 217233, tag last modified 2025-01-20 23:37:20)
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 115384 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"192335307*2^25000+5129" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 192335307*2^25000+5129 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 7+sqrt(11) Calling N+1 BLS with factored part 0.06% and helper 0.06% (0.25% proof) 192335307*2^25000+5129 is Fermat and Lucas PRP! (8.9279s+0.0003s) [Elapsed time: 9.00 seconds] modified 2020-07-07 22:30:18 created 2013-09-04 23:23:11 id 160871
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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