648621027630345 · 2253825 - 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: | 648621027630345 · 2253825 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Sophie Germain (2p+1) |
| Proof-code(s): (*): | x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown |
| Decimal Digits: | 76424 (log10 is 76423.750640434) |
| Rank (*): | 54800 (digit rank is 1) |
| Entrance Rank (*): | 16312 |
| Currently on list? (*): | short |
| Submitted: | 11/18/2009 18:17:18 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 90908 |
| Status Flags: | none |
| Score (*): | 38.7256 (normalized score 0.0016) |
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 7
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 210550, 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 90908 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 648621027630345 2 253825 -1 2>&1 [Elapsed time: 9.254 seconds] modified 2020-07-07 22:30:36 created 2009-11-18 18:18:01 id 111189
field value prime_id 90908 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/llr.pl 648621027630345*2^253825-1 2>&1 Starting Lucas Lehmer Riesel prime test of 648621027630345*2^253825-1 Using Zero Padded IBDWT : Mersenne fftlen = 12288, Used fftlen = 24576 V1 = 11 ; Computing U0... V1 = 11 ; Computing U0...done. Starting Lucas-Lehmer loop... 648621027630345*2^253825-1 is prime! Time : 174.942 sec. [Elapsed time: 2.92 minutes] modified 2020-07-07 22:30:36 created 2009-11-18 18:23:02 id 111191
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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