primU(34593)
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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:primU(34593)
Verification status (*):PRP
Official Comment:Fibonacci primitive part, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:4444   (log10 is 4443.7962385907)
Rank (*):82445 (digit rank is 1)
Entrance Rank (*):44925
Currently on list? (*):short
Submitted:8/25/2007 16:24:33 CDT
Last modified:8/25/2007 23:58:48 CDT
Database id:82036
Status Flags:Verify
Score (*):29.9227 (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.
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 20
Subcategory: "Fibonacci Primitive Part"
(archival tag id 195438, tag last modified 2016-07-12 12:50:05)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 418
Subcategory: "ECPP"
(archival tag id 195437, tag last modified 2017-11-16 23:50:19)

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_id82036
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
6255162415...2154259338.........3582467832027333 1/1


trial factoring to 1192990
6255162415...3806420161 has no small factor.
[Elapsed time: 3.040 seconds]
modified2007-09-12 06:50:18
created2007-08-25 16:52:02
id93191

fieldvalue
prime_id82036
person_id9
machineRedHat P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 6255162415...3806420161 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1792,21) to FFT(1792,20)
Reduced from FFT(1792,20) to FFT(1792,19)
Reduced from FFT(1792,19) to FFT(1792,18)
Reduced from FFT(1792,18) to FFT(1792,17)
29532 bit request FFT size=(1792,17)
Running N+1 test using discriminant 31, base 15+sqrt(31)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(1792,21) to FFT(1792,20)
Reduced from FFT(1792,20) to FFT(1792,19)
Reduced from FFT(1792,19) to FFT(1792,18)
Reduced from FFT(1792,18) to FFT(1792,17)
29540 bit request FFT size=(1792,17)
Calling N-1 BLS with factored part 1.63% and helper 0.03% (4.93% proof)
6255162415...3806420161 is Fermat and Lucas PRP! (8.0900s+0.0100s)
[Elapsed time: 9 seconds]
modified2007-08-25 23:58:48
created2007-08-25 23:58:39
id93199

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