642 · Bern(1802)/15720728189
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:642 · Bern(1802)/15720728189
Verification status (*):PRP
Official Comment:Irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:3641   (log10 is 3640.89042614)
Rank (*):83652 (digit rank is 1)
Entrance Rank (*):32315
Currently on list? (*):short
Submitted:11/19/2003 21:04:44 CDT
Last modified:11/19/2003 21:04:44 CDT
Database id:67292
Status Flags:Verify
Score (*):29.303 (normalized score 0)

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.
Irregular Primes (archivable *)
Prime on list: yes, rank 17
Subcategory: "Irregular Primes"
(archival tag id 178321, tag last modified 2016-11-18 02:20:40)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 500
Subcategory: "ECPP"
(archival tag id 178322, tag last modified 2017-11-27 10:20:19)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): 
certificate

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.
fieldvalue
prime_id67292
person_id9
machineLinux P4 2.8GHz
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7770091554...0081100873 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 960573
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24198 bit request FFT size=(1536,16)
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24198 bit request FFT size=(1536,16)
Running N+1 test using discriminant 23, base 2+sqrt(23)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1536,21) to FFT(1536,20)
Reduced from FFT(1536,20) to FFT(1536,19)
Reduced from FFT(1536,19) to FFT(1536,18)
Reduced from FFT(1536,18) to FFT(1536,17)
Reduced from FFT(1536,17) to FFT(1536,16)
24206 bit request FFT size=(1536,16)
Calling N-1 BLS with factored part 0.08% and helper 0.05% (0.31% proof)
7770091554...0081100873 is Fermat and Lucas PRP! (12.3940s+0.0017s)
modified2003-11-19 21:12:11
created2003-11-19 21:11:58
id72223

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.