Phi(427, - 1028)
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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(427, - 1028)
Verification status (*):PRP
Official Comment:Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):FE9 : Morain, Water, Broadhurst, FastECPP
Decimal Digits:10081   (log10 is 10080)
Rank (*):72728 (digit rank is 6)
Entrance Rank (*):41352
Currently on list? (*):short
Submitted:5/9/2009 08:01:48 CDT
Last modified:5/9/2009 12:49:15 CDT
Database id:88149
Status Flags:Verify
Score (*):32.4648 (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 153
Subcategory: "ECPP"
(archival tag id 210440, tag last modified 2017-10-14 12:20:20)
Unique (archivable *)
Prime on list: yes, rank 8
Subcategory: "Unique"
(archival tag id 210441, 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.

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_id88149
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f36{3416} -q"Phi(427,-10^28)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Factoring numbers to 36% of normal.
Using modular factorization: {3416}
trial factoring to 2383595230
Phi(427,-10^28) has no small factor.
[Elapsed time: 1.317 seconds]
modified2011-12-27 16:48:44
created2009-05-09 08:05:01
id105660

fieldvalue
prime_id88149
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -t -q"Phi(427,-10^28)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(427,-10^28) [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(4096,21) to FFT(4096,20)
Reduced from FFT(4096,20) to FFT(4096,19)
Reduced from FFT(4096,19) to FFT(4096,18)
Reduced from FFT(4096,18) to FFT(4096,17)
66980 bit request FFT size=(4096,17)
Running N-1 test using base 53
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(4096,21) to FFT(4096,20)
Reduced from FFT(4096,20) to FFT(4096,19)
Reduced from FFT(4096,19) to FFT(4096,18)
Reduced from FFT(4096,18) to FFT(4096,17)
66980 bit request FFT size=(4096,17)
Calling Brillhart-Lehmer-Selfridge with factored part 1.64%
Phi(427,-10^28) is PRP! (23.7300s+0.0000s)
[Elapsed time: 24.00 seconds]
modified2009-05-25 07:25:55
created2009-05-09 08:08:01
id105661

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.