137211941292195 · 2171961 - 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: | 137211941292195 · 2171961 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Sophie Germain (2p+1) |
| Proof-code(s): (*): | x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown |
| Decimal Digits: | 51780 (log10 is 51779.556476283) |
| Rank (*): | 61323 (digit rank is 1) |
| Entrance Rank (*): | 10176 |
| Currently on list? (*): | yes |
| Submitted: | 5/4/2006 13:11:01 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 77714 |
| Status Flags: | none |
| Score (*): | 37.5249 (normalized score 0.0004) |
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.
- Sophie Germain (2p+1) (archivable *)
- Prime on list: yes, rank 20
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 189937, tag last modified 2024-10-04 20:37:13)
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 77714 person_id 9 machine WinXP P4 2.2GHz M what prime notes Command: pfgw.exe -n -f -tp -q"137211941292195*2^171961-1" 2>&1 PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 137211941292195*2^171961-1 [N+1, Brillhart-Lehmer-Selfridge] trial factoring to 16858146 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling Brillhart-Lehmer-Selfridge with factored part 99.97% 137211941292195*2^171961-1 is prime! (2062.0910s+0.0417s) [Elapsed time: 2063 seconds] modified 2020-07-07 22:30:42 created 2006-05-04 13:19:34 id 84238
field value prime_id 77714 person_id 9 machine GenToo P3 400MHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 137211941292195 2 171961 -1 2>&1 [Elapsed time: 9.260 seconds] modified 2020-07-07 22:30:42 created 2006-07-07 15:38:44 id 85233
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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