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.
|Verification status (*):||PRP|
|Official Comment (*):||Fibonacci cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c41 : Andersen, Rosenthal, Primo|
|Decimal Digits:||6395 (log10 is 6394.45286292)|
|Rank (*):||84583 (digit rank is 1)|
|Entrance Rank (*):||35038|
|Currently on list? (*):||no|
|Submitted:||12/4/2005 20:05:07 CDT|
|Last modified:||12/4/2005 20:23:36 CDT|
|Score (*):||31.0531 (normalized score 0)|
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.
- Fibonacci cofactor (archivable *)
- Prime on list: no, rank 24
Subcategory: "Fibonacci cofactor"
(archival tag id 194825, tag last modified 2022-07-03 06:37:26)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 397
(archival tag id 194824, tag last modified 2022-07-03 06:37:26)
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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 76368 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"U(30671)/1141737296775689" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing U(30671)/1141737296775689 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1770815 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 42492 bit request FFT size=(2560,17) Running N+1 test using discriminant 7, base 1+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) 42500 bit request FFT size=(2560,17) Calling N-1 BLS with factored part 0.16% and helper 0.01% (0.50% proof) U(30671)/1141737296775689 is Fermat and Lucas PRP! (34.7709s+0.0014s) [Elapsed time: 35 seconds] modified 2020-07-07 17:30:43 created 2005-12-04 20:23:01 id 81577