U(10803, 1, 4081) - U(10803, 1, 4080)
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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(10803, 1, 4081) - U(10803, 1, 4080)
Verification status (*):PRP
Official Comment:Lehmer number, cyclotomy
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:16457   (log10 is 16456.860999069)
Rank (*):66345 (digit rank is 1)
Entrance Rank (*):24060
Currently on list? (*):short
Submitted:12/6/2005 08:02:15 CDT
Last modified:12/6/2005 10:56:00 CDT
Database id:76387
Status Flags:Verify
Score (*):33.983 (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 16
Subcategory: "Lehmer number"
(archival tag id 192433, tag last modified 2017-06-28 15:50:31)
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 7
Subcategory: "Cyclotomy Proof"
(archival tag id 192432, tag last modified 2009-02-12 20:01:27)

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): 
WL proof with 3 titanic ECPP helpers. For a certificate of proof see http://physics.open.ac.uk/~dbroadhu/cert/b8161a.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_id76387
person_id9
machineLinux P4 2.8GHz
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 7261044003...8886378561 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 4919292
Running N-1 test using base 41
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)
109346 bit request FFT size=(7168,16)
Running N-1 test using base 43
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)
109346 bit request FFT size=(7168,16)
Running N+1 test using discriminant 61, base 15+sqrt(61)
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)
109354 bit request FFT size=(7168,16)
Calling N-1 BLS with factored part 1.12% and helper 0.41% (3.76% proof)
7261044003...8886378561 is Fermat and Lucas PRP! (409.1077s+0.0719s)
[Elapsed time: 409 seconds]
modified2005-12-06 10:56:00
created2005-12-06 10:49:11
id81601

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