Phi(3243, - 2399401)/33320592661
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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(3243, - 2399401)/33320592661
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:12903   (log10 is 12902.805426372)
Rank (*):69814 (digit rank is 1)
Entrance Rank (*):47009
Currently on list? (*):no
Submitted:12/12/2010 12:54:32 CDT
Last modified:12/12/2010 13:20:28 CDT
Database id:96871
Status Flags:Verify
Score (*):33.2297 (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 62
Subcategory: "ECPP"
(archival tag id 213015, tag last modified 2017-06-04 14:20:21)

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.

Tom Wu writes (11 Sep 2014): 
This prime is a key part of the primality proof of the generalized repunit prime N=Phi(12973,1549); it divides N-1 and provides about 31.2% of its prime factorization.

The Primo certificate took about 7 months to generate using multiple processors to accelerate Phase 1 and run Phase 2 concurrently. The certificate is available at:

http://www.ellipsa.eu/public/primo/files/ecpp12903.zip
The expression for this prime can also be written as Phi(12972,1549)/(12973*2568457).

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_id96871
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"Phi(3243,-2399401)/33320592661" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 3783937
Phi(3243,-2399401)/33320592661 has no small factor.
[Elapsed time: 4.344 seconds]
modified2011-12-27 16:48:35
created2010-12-12 13:05:02
id123132

fieldvalue
prime_id96871
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"Phi(3243,-2399401)/33320592661" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(3243,-2399401)/33320592661 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(5120,21) to FFT(5120,20)
Reduced from FFT(5120,20) to FFT(5120,19)
Reduced from FFT(5120,19) to FFT(5120,18)
Reduced from FFT(5120,18) to FFT(5120,17)
85734 bit request FFT size=(5120,17)
Running N+1 test using discriminant 7, base 1+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(5120,21) to FFT(5120,20)
Reduced from FFT(5120,20) to FFT(5120,19)
Reduced from FFT(5120,19) to FFT(5120,18)
Reduced from FFT(5120,18) to FFT(5120,17)
85742 bit request FFT size=(5120,17)
Calling N-1 BLS with factored part 0.08% and helper 0.06% (0.30% proof)
Phi(3243,-2399401)/33320592661 is Fermat and Lucas PRP! (77.2900s+0.0100s)
[Elapsed time: 77.00 seconds]
modified2011-01-18 10:15:30
created2010-12-12 13:08:02
id123134

Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.