400254 · 127400254 + 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: | 400254 · 127400254 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Cullen |
| Proof-code(s): (*): | g407 : HermleGC, MultiSieve, PRP, Proth.exe |
| Decimal Digits: | 842062 (log10 is 842061.45686319) |
| Rank (*): | 3608 (digit rank is 1) |
| Entrance Rank (*): | 103 |
| Currently on list? (*): | yes |
| Submitted: | 6/4/2013 03:32:55 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 114324 |
| Status Flags: | none |
| Score (*): | 46.1055 (normalized score 2.6581) |
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 Cullen (archivable *)
- Prime on list: no, rank 28
Subcategory: "Generalized Cullen"
(archival tag id 217180, tag last modified 2024-08-17 05:37:11)
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 114324 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 400254 127 400254 1 2>&1 [Elapsed time: 9.674 seconds] modified 2020-07-07 22:30:19 created 2013-06-04 03:35:02 id 159024
field value prime_id 114324 person_id 9 machine WinXP Dual Core 2.6GHz 64-bit Laptop what prime notes Command: pfgw64.exe -t -q"400254*127^400254+1" 2>&1 PFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing 400254*127^400254+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 400254*127^400254+1 is prime! (9832.4878s+0.0405s) [Elapsed time: 9834 seconds] modified 2020-07-07 22:30:19 created 2013-06-04 13:04:29 id 159033
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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