21203793 - 2601897 + 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: | 21203793 - 2601897 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Gaussian Mersenne norm 37, generalized unique |
| Proof-code(s): (*): | L192 : Jaworski, LLR |
| Decimal Digits: | 362378 (log10 is 362377.80157033) |
| Rank (*): | 19757 (digit rank is 1) |
| Entrance Rank (*): | 98 |
| Currently on list? (*): | yes |
| Submitted: | 9/21/2006 01:03:49 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 78531 |
| Status Flags: | none |
| Score (*): | 43.516 (normalized score 0.1994) |
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 5
Subcategory: "Gaussian Mersenne norm"
(archival tag id 187093, tag last modified 2023-03-11 15:53:59)- Generalized Unique (archivable *)
- Prime on list: no, rank 125
Subcategory: "Generalized Unique"
(archival tag id 224189, 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 78531 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"2^1203793-2^601897+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 134377248 2^1203793-2^601897+1 has no small factor. [Elapsed time: 3281.263 seconds] modified 2020-07-07 22:30:42 created 2006-09-21 01:22:01 id 86160
field value prime_id 78531 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"2^1203793-2^601897+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^1203793-2^601897+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(163840,20) to FFT(163840,19) Reduced from FFT(163840,19) to FFT(163840,18) Reduced from FFT(163840,18) to FFT(163840,17) Reduced from FFT(163840,17) to FFT(163840,16) 2407594 bit request FFT size=(163840,16) Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^1203793-2^601897+1 is prime! (-363.8238s+0.0000s) [Elapsed time: 27998 seconds] modified 2020-07-07 22:30:42 created 2006-09-21 01:23:03 id 86161
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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