78284791145 · 2371# + 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: | 78284791145 · 2371# + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Arithmetic progression (6,d=6350457699*2371#) |
| Proof-code(s): (*): | p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW |
| Decimal Digits: | 1014 (log10 is 1013.6438600912) |
| Rank (*): | 131595 (digit rank is 1301) |
| Entrance Rank (*): | 103856 |
| Currently on list? (*): | yes |
| Submitted: | 4/11/2013 20:52:29 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 112544 |
| Status Flags: | none |
| Score (*): | 25.3143 (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.
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: yes, rank 5, weight 40.818531577922
Subcategory: "6/9"
(archival tag id 236796, tag last modified 2025-05-23 12:37:10)
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 112544 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 78284791145 2371 # 1 2>&1 [Elapsed time: 144.481 seconds] modified 2020-07-07 22:30:21 created 2013-04-11 21:05:30 id 155418
field value prime_id 112544 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"78284791145*2371#+1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 78284791145*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.59% 78284791145*2371#+1 is prime! (0.5722s+0.0005s) [Elapsed time: 0.00 seconds] modified 2020-07-07 22:30:21 created 2013-04-11 21:08:05 id 155425
Query times: 0.0011 seconds to select prime, 0.0015 seconds to seek comments.
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