277947065536 + 1
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: | 277947065536 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Proof-code(s): (*): | p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW |
| Decimal Digits: | 422312 (log10 is 422311.49303399) |
| Rank (*): | 15311 (digit rank is 1) |
| Entrance Rank (*): | 503 |
| Currently on list? (*): | no |
| Submitted: | 7/25/2012 16:27:17 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Removed (*): | 4/23/2019 11:59:06 UTC |
| Database id: | 108493 |
| Status Flags: | none |
| Score (*): | 43.9863 (normalized score 0.2287) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 4869
Subcategory: "Generalized Fermat"
(archival tag id 214446, tag last modified 2025-05-12 22:37:13)
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 108493 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 2779470 65536 1 2>&1 [Elapsed time: 7.869 seconds] modified 2020-07-07 22:30:25 created 2012-07-25 16:35:01 id 146571
field value prime_id 108493 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -t -q"2779470^65536+1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 2779470^65536+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 39.42% 2779470^65536+1 is prime! (10665.9174s+0.1082s) [Elapsed time: 2.96 hours] modified 2020-07-07 22:30:25 created 2012-07-25 16:52:33 id 146572
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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