Phi(4029, - 1000)
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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:Phi(4029, - 1000)
Verification status (*):PRP
Official Comment:Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c47 : Chandler, Primo
Decimal Digits:7488   (log10 is 7487.99956592295)
Rank (*):76949 (digit rank is 1)
Entrance Rank (*):45763
Currently on list? (*):short
Submitted:8/18/2009 07:45:51 CDT
Last modified:8/18/2009 08:20:23 CDT
Database id:89682
Status Flags:Verify
Score (*):31.543 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 273
Subcategory: "ECPP"
(archival tag id 210494, tag last modified 2018-11-04 20:50:19)
Unique (archivable *)
Prime on list: yes, rank 12
Subcategory: "Unique"
(archival tag id 210495, tag last modified 2014-05-20 07:51:28)

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.

Ray Chandler writes (11 Sep 2014): 

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(4029,-1000)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 2101180
Phi(4029,-1000) has no small factor.
[Elapsed time: 1.478 seconds]
modified2011-12-27 16:48:42
created2009-08-18 07:48:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"Phi(4029,-1000)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(4029,-1000) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 47
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3072,21) to FFT(3072,20)
Reduced from FFT(3072,20) to FFT(3072,19)
Reduced from FFT(3072,19) to FFT(3072,18)
Reduced from FFT(3072,18) to FFT(3072,17)
49758 bit request FFT size=(3072,17)
Calling Brillhart-Lehmer-Selfridge with factored part 0.83%
Phi(4029,-1000) is PRP! (7.6400s+0.0000s)
[Elapsed time: 8.00 seconds]
modified2009-11-24 13:57:51
created2009-08-18 07:53:01

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.