Phi(7357, - 10)
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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(7357, - 10)
Verification status (*):PRP
Official Comment:Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c33 : Chaglassian, Primo
Decimal Digits:6301   (log10 is 6300.04139264173)
Rank (*):78098 (digit rank is 2)
Entrance Rank (*):29664
Currently on list? (*):short
Submitted:5/29/2004 03:50:04 CDT
Last modified:5/29/2004 03:50:04 CDT
Database id:70533
Status Flags:Verify
Score (*):31.0069 (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.
Unique (archivable *)
Prime on list: yes, rank 17
Subcategory: "Unique"
(archival tag id 210374, tag last modified 2014-05-20 07:51:28)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 302
Subcategory: "ECPP"
(archival tag id 210373, tag last modified 2017-11-27 10:20:19)

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.

Raffi Chaglassian 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_id70533
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -t -q"Phi(7357,-10)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(7357,-10) [N-1, Brillhart-Lehmer-Selfridge]
trial factoring to 1742546
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
41866 bit request FFT size=(2560,17)
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
41866 bit request FFT size=(2560,17)
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
41866 bit request FFT size=(2560,17)
Running N-1 test using base 11
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
41866 bit request FFT size=(2560,17)
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(2560,21) to FFT(2560,20)
Reduced from FFT(2560,20) to FFT(2560,19)
Reduced from FFT(2560,19) to FFT(2560,18)
Reduced from FFT(2560,18) to FFT(2560,17)
41866 bit request FFT size=(2560,17)
Calling Brillhart-Lehmer-Selfridge with factored part 1.32%
Phi(7357,-10) is PRP! (39.4842s+0.0011s)
modified2004-08-05 12:46:56
created2004-05-29 03:53:00
id75492

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