(U(9275, 1, 3961) + U(9275, 1, 3960))/(U(9275, 1, 45) + U(9275, 1, 44))
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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:(U(9275, 1, 3961) + U(9275, 1, 3960))/(U(9275, 1, 45) + U(9275, 1, 44))
Verification status (*):PRP
Official Comment:Lehmer primitive part
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):x38 : Broadhurst, Primo, OpenPFGW
Decimal Digits:15537   (log10 is 15536.001284243)
Rank (*):61510 (digit rank is 1)
Entrance Rank (*):35575
Currently on list? (*):short
Submitted:5/10/2009 04:19:03 CDT
Last modified:5/10/2009 04:50:21 CDT
Database id:88162
Status Flags:Verify
Score (*):33.8047 (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.
Lehmer primitive part (archivable *)
Prime on list: yes, rank 7
Subcategory: "Lehmer primitive part"
(archival tag id 210442, tag last modified 2013-02-05 17:20:28)

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 (10 May 2009): 
BLS tests were performed with factorization fractions of 31.10% in N-1 and 8.65% in N+1. The proof depends upon the primality of helpers with 638, 1034 and 3490 digits, proven by Primo. Because the index 3961+3960=89^2 is the square of a prime, this Lehmer primitive part is also the unique prime in the Lehmer sequence U(P,1,45)+U(P,1,44) with P=V(9275,1,89). At time of proof, it was the largest known unique Lehmer prime and also the largest known prime that is a Lehmer primitive part.

David Broadhurst writes (10 May 2009): 
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_id88162
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
(lucasU(9275,1,3961)+luca.........,1,45)+lucasU(92 1/1


trial factoring to 4623227
(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) has no small factor.
[Elapsed time: 6.252 seconds]
modified2011-12-27 16:48:44
created2009-05-10 04:35:01
id105687

fieldvalue
prime_id88162
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44))" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) [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(6144,21) to FFT(6144,20)
Reduced from FFT(6144,20) to FFT(6144,19)
Reduced from FFT(6144,19) to FFT(6144,18)
Reduced from FFT(6144,18) to FFT(6144,17)
103228 bit request FFT size=(6144,17)
Running N-1 test using base 7
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(6144,21) to FFT(6144,20)
Reduced from FFT(6144,20) to FFT(6144,19)
Reduced from FFT(6144,19) to FFT(6144,18)
Reduced from FFT(6144,18) to FFT(6144,17)
103228 bit request FFT size=(6144,17)
Running N+1 test using discriminant 23, base 1+sqrt(23)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(6144,21) to FFT(6144,20)
Reduced from FFT(6144,20) to FFT(6144,19)
Reduced from FFT(6144,19) to FFT(6144,18)
Reduced from FFT(6144,18) to FFT(6144,17)
103236 bit request FFT size=(6144,17)
Calling N-1 BLS with factored part 0.57% and helper 0.29% (2.01% proof)
(lucasU(9275,1,3961)+lucasU(9275,1,3960))/(lucasU(9275,1,45)+lucasU(9275,1,44)) is Fermat and Lucas PRP! (150.4400s+0.0100s)
[Elapsed time: 2.77 minutes]
modified2009-05-25 07:25:55
created2009-05-10 04:23:01
id105686

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