514495232768 + 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: | 514495232768 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Proof-code(s): (*): | p347 : Vogel, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW |
| Decimal Digits: | 219919 (log10 is 219918.54333469) |
| Rank (*): | 31534 (digit rank is 1) |
| Entrance Rank (*): | 4993 |
| Currently on list? (*): | no |
| Submitted: | 3/24/2012 13:07:58 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Removed (*): | 3/25/2012 00:55:45 UTC |
| Database id: | 105801 |
| Status Flags: | none |
| Score (*): | 41.9804 (normalized score 0.0307) |
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 4989
Subcategory: "Generalized Fermat"
(archival tag id 214245, 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 105801 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"5144952^32768+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 5144952^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 79.43% 5144952^32768+1 is prime! (5799.7192s+0.0125s) [Elapsed time: 1.61 hours] modified 2020-07-07 22:30:27 created 2012-03-24 13:08:01 id 141184
field value prime_id 105801 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 5144952 32768 1 2>&1 [Elapsed time: 7.661 seconds] modified 2020-07-07 22:30:27 created 2012-03-24 13:18:01 id 141186
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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