
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 
Unofficial Comments:  This prime has 2 user comments below. 
Proofcode(s): (*):  x38 : Broadhurst, Primo, OpenPFGW 
Decimal Digits:  8622 (log_{10} is 8621.7756615986) 
Rank (*):  74167 (digit rank is 1) 
Entrance Rank (*):  42682 
Currently on list? (*):  no 
Submitted:  5/2/2009 11:13:35 CDT 
Last modified:  5/2/2009 11:50:36 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"
(archival tag id 208992, tag last modified 20160614 19:50:41)
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.
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.
field  value 
prime_id  87993 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /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]

modified  20111227 16:48:44 
created  20090502 11:18:02 
id  105344 

field  value 
prime_id  87993 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /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)) [N1/N+1, BrillhartLehmerSelfridge] Running N1 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 N1 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 N1 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 N1 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 N1 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]

modified  20090525 07:25:56 
created  20090502 11:23:01 
id  105345 

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
