(U(2948, 1, 2521) - U(2948, 1, 2520))/(U(2948, 1, 36) - U(2948, 1, 35)) (Another of the Prime Pages' resources)

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(2948, 1, 2521) - U(2948, 1, 2520))/(U(2948, 1, 36) - U(2948, 1, 35))
Verification status (*):PRP
Official Comment:Lehmer primitive part
Proof-code(s): (*):x38 : Broadhurst, Primo, OpenPFGW
Decimal Digits:8622   (log10 is 8621.7756615986)
Rank (*):75000 (digit rank is 1)
Entrance Rank (*):42682
Currently on list? (*):no
Submitted:5/2/2009 11:13:35 CDT
Database id:87993
Status Flags:Verify
Score (*):31.9803 (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: no, rank 53
Subcategory: "Lehmer primitive part"

David Broadhurst writes (11 Sep 2014):
 BLS tests were performed with factorization fractions of 26.68% in N-1 and 8.61% in N+1, permitting a proof by OpenLenstra. Because the index 2521+2520=71^2 is the square of a prime, this Lehmer primitive part is also the unique prime in the Lehmer sequence U(P,1,36)-U(P,1,35) with P=V(2948,1,71). At time of proof, it was the largest known unique Lehmer prime.

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_id87993
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(lucasU(2948,1,2521)-lucasU(2948,1,2520))/(lucasU(2948,1,36)-lucasU(2948,1,35))" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
(lucasU(2948,1,2521)-luca.........,1,36)-lucasU(29 1/1

trial factoring to 2447567
(lucasU(2948,1,2521)-lucasU(2948,1,2520))/(lucasU(2948,1,36)-lucasU(2948,1,35)) has no small factor.
[Elapsed time: 1.952 seconds]
modified2011-12-27 16:48:44
created2009-05-02 11:18:02
id105344

fieldvalue
prime_id87993
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(lucasU(2948,1,2521)-lucasU(2948,1,2520))/(lucasU(2948,1,36)-lucasU(2948,1,35))" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (lucasU(2948,1,2521)-lucasU(2948,1,2520))/(lucasU(2948,1,36)-lucasU(2948,1,35)) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57290 bit request FFT size=(3584,17)
Running N-1 test using base 29
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57290 bit request FFT size=(3584,17)
Running N-1 test using base 31
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57290 bit request FFT size=(3584,17)
Running N-1 test using base 37
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57290 bit request FFT size=(3584,17)
Running N+1 test using discriminant 43, base 12+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57298 bit request FFT size=(3584,17)
Running N+1 test using discriminant 43, base 16+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57298 bit request FFT size=(3584,17)
Running N+1 test using discriminant 43, base 19+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57298 bit request FFT size=(3584,17)
Running N+1 test using discriminant 43, base 21+sqrt(43)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(3584,21) to FFT(3584,20)
Reduced from FFT(3584,20) to FFT(3584,19)
Reduced from FFT(3584,19) to FFT(3584,18)
Reduced from FFT(3584,18) to FFT(3584,17)
57298 bit request FFT size=(3584,17)
Calling N-1 BLS with factored part 1.23% and helper 0.56% (4.24% proof)
(lucasU(2948,1,2521)-lucasU(2948,1,2520))/(lucasU(2948,1,36)-lucasU(2948,1,35)) is Fermat and Lucas PRP! (140.0700s+0.0000s)
[Elapsed time: 2.42 minutes]
modified2009-05-25 07:25:56
created2009-05-02 11:23:01
id105345

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.