U(9657, 1, 4321) - U(9657, 1, 4320)
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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:U(9657, 1, 4321) - U(9657, 1, 4320)
Verification status (*):PRP
Official Comment:Lehmer number
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x23 : Renze, Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:17215   (log10 is 17214.5183745831)
Rank (*):65923 (digit rank is 1)
Entrance Rank (*):23731
Currently on list? (*):short
Submitted:12/4/2005 23:48:46 CDT
Last modified:12/5/2005 03:41:58 CDT
Database id:76372
Status Flags:Verify
Score (*):34.1222 (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.
Lehmer number (archivable *)
Prime on list: yes, rank 14
Subcategory: "Lehmer number"
(archival tag id 192391, tag last modified 2017-06-28 15:50:31)

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): 
CHG proof with ECPP helpers. For a certificate of proof see http://physics.open.ac.uk/~dbroadhu/cert/b8641.zip

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_id76372
person_id9
machineLinux P4 2.8GHz
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 3298941263...1824940801 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 5163802
Running N-1 test using base 59
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
Reduced from FFT(7168,18) to FFT(7168,17)
Reduced from FFT(7168,17) to FFT(7168,16)
114380 bit request FFT size=(7168,16)
Running N-1 test using base 67
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
Reduced from FFT(7168,18) to FFT(7168,17)
Reduced from FFT(7168,17) to FFT(7168,16)
114380 bit request FFT size=(7168,16)
Running N-1 test using base 83
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
Reduced from FFT(7168,18) to FFT(7168,17)
Reduced from FFT(7168,17) to FFT(7168,16)
114380 bit request FFT size=(7168,16)
Running N+1 test using discriminant 101, base 18+sqrt(101)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(7168,21) to FFT(7168,20)
Reduced from FFT(7168,20) to FFT(7168,19)
Reduced from FFT(7168,19) to FFT(7168,18)
Reduced from FFT(7168,18) to FFT(7168,17)
Reduced from FFT(7168,17) to FFT(7168,16)
114388 bit request FFT size=(7168,16)
Calling N-1 BLS with factored part 1.16% and helper 0.28% (3.77% proof)
3298941263...1824940801 is Fermat and Lucas PRP! (441.2670s+0.0426s)
[Elapsed time: 442 seconds]
modified2005-12-05 03:41:58
created2005-12-05 03:34:36
id81586

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.