"21808089752589180735...(1265 other digits)...35084386334974361601"
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: | "21808089752589180735...(1265 other digits)...35084386334974361601" |
---|---|
Verification status (*): | Proven |
Official Comment (*): | 14-Carmichael factor (14) |
Unofficial Comments: | This prime has 1 user comment below. |
Proof-code(s): (*): | p44 : Broadhurst, OpenPFGW |
Decimal Digits: | 1305 (log10 is 1304.33861763) |
Rank (*): | 113227 (digit rank is 32) |
Entrance Rank (*): | 49886 |
Currently on list? (*): | no |
Submitted: | 5/16/2004 20:41:52 UTC |
Last modified: | 3/11/2023 15:54:10 UTC |
Database id: | 70369 |
Blob database id: | 118 |
Status Flags: | none |
Score (*): | 26.1028 (normalized score 0) |
Description: (from blob table id=118)
174638735017501402241941925786257726099327047877470790543582 * 1234578514375589600139299461309891215472748486893861616781823576745550941638810434994756075634238711959503055472046080 * 127265758603053652854671144842647200096979469577422603773338025370475153 * 2477# + 1
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.
- n-Carmichael factor (tolerated *)
- Prime on list: no, rank 1
Subcategory: "14-Carmichael factor (14)"
(archival tag id 180350, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
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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 70369 person_id 9 machine Linux P4 2.8GHz what prime notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2180808975...4974361601 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 312945 Running N-1 test using base 2503 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8674 bit request FFT size=(512,18) Running N-1 test using base 2531 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8674 bit request FFT size=(512,18) Running N+1 test using discriminant 2557, base 78+sqrt(2557) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8682 bit request FFT size=(512,18) Calling N-1 BLS with factored part 86.91% and helper 0.30% (261.06% proof) 2180808975...4974361601 is prime! (7.7558s+0.0006s) modified 2020-07-07 22:30:45 created 2004-06-02 19:55:33 id 75528
Query times: 0.0002 seconds to select prime, 0.0006 seconds to seek comments.
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