2 · 19166971 + 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: | 2 · 19166971 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides Phi(191^66971,2) |
| Proof-code(s): (*): | g404 : Taniguchi, Proth.exe |
| Decimal Digits: | 152764 (log10 is 152763.38666794) |
| Rank (*): | 40835 (digit rank is 1) |
| Entrance Rank (*): | 700 |
| Currently on list? (*): | no |
| Submitted: | 10/21/2006 00:25:23 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 78694 |
| Status Flags: | none |
| Score (*): | 40.8591 (normalized score 0.0162) |
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.
- Divides Phi (archivable *)
- Prime on list: no, rank 60
Subcategory: "Divides Phi"
(archival tag id 187399, tag last modified 2023-03-11 15:53:59)
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 78694 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 2 191 66971 1 2>&1 [Elapsed time: 8.545 seconds] modified 2020-07-07 22:30:42 created 2006-10-21 00:52:02 id 86485
field value prime_id 78694 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"2*191^66971+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2*191^66971+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1014946 bit request FFT size=(65536,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 2*191^66971+1 is prime! (-1210.4773s+0.0300s) [Elapsed time: 3162 seconds] modified 2020-07-07 22:30:42 created 2006-10-21 00:53:02 id 86486
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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