
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. 
Proofcode(s): (*):  c8 : Water, Broadhurst, Primo 
Decimal Digits:  4444 (log_{10} is 4443.7962385907) 
Rank (*):  83841 (digit rank is 1) 
Entrance Rank (*):  44925 
Currently on list? (*):  no 
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: no, rank 22
Subcategory: "Fibonacci Primitive Part"
(archival tag id 195438, tag last modified 20180417 09:50:29)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 432
Subcategory: "ECPP"
(archival tag id 195437, tag last modified 20180702 08:50:19)
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.
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.
field  value 
prime_id  82036 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  PFGW 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]

modified  20070912 06:50:18 
created  20070825 16:52:02 
id  93191 

field  value 
prime_id  82036 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 6255162415...3806420161 [N1/N+1, BrillhartLehmerSelfridge] Running N1 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 N1 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]

modified  20070825 23:58:48 
created  20070825 23:58:39 
id  93199 

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.
