21667321 - 2833661 + 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: | 21667321 - 2833661 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Gaussian Mersenne norm 38, generalized unique |
| Proof-code(s): (*): | L137 : Jaworski, Rieselprime, LLR |
| Decimal Digits: | 501914 (log10 is 501913.63340047) |
| Rank (*): | 9209 (digit rank is 1) |
| Entrance Rank (*): | 109 |
| Currently on list? (*): | short |
| Submitted: | 1/14/2011 07:06:44 UTC |
| Last modified: | 9/5/2023 22:00:05 UTC |
| Database id: | 97416 |
| Status Flags: | none |
| Score (*): | 44.5168 (normalized score 0.6263) |
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.
- Gaussian Mersenne norm (archivable *)
- Prime on list: yes, rank 4
Subcategory: "Gaussian Mersenne norm"
(archival tag id 213060, tag last modified 2023-03-11 15:53:59)- Generalized Unique (archivable *)
- Prime on list: no, rank 82
Subcategory: "Generalized Unique"
(archival tag id 224146, tag last modified 2023-12-18 15:37:22)
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 97416 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"2^1667321-2^833661+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^1667321-2^833661+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3334650 bit request FFT size=(229376,16) Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^1667321-2^833661+1 is prime! (56794.4485s+0.0014s) [Elapsed time: 15.78 hours] modified 2020-07-07 22:30:32 created 2011-01-14 07:08:01 id 124221
field value prime_id 97416 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"2^1667321-2^833661+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 189921883 2^1667321-2^833661+1 has no small factor. [Elapsed time: 6036.135 seconds] modified 2020-07-07 22:30:32 created 2011-01-14 07:18:02 id 124222
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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