
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(14257,  1, 3779) 
Verification status (*):  PRP 
Official Comment:  Generalized Lucas number, cyclotomy 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  x25 : Water, Broadhurst, Primo, OpenPFGW 
Decimal Digits:  15694 (log_{10} is 15693.9183572707) 
Rank (*):  67108 (digit rank is 1) 
Entrance Rank (*):  17510 
Currently on list? (*):  short 
Submitted:  1/19/2004 10:12:27 CDT 
Last modified:  1/19/2004 10:12:27 CDT 
Database id:  68432 
Status Flags:  Verify 
Score (*):  33.836 (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.
 Cyclotomy Proof (tolerated *)
 Prime on list: no, rank 10
Subcategory: "Cyclotomy Proof"
(archival tag id 192476, tag last modified 20090212 20:01:27)  Generalized Lucas Number (archivable *)
 Prime on list: yes, rank 11
Subcategory: "Generalized Lucas Number"
(archival tag id 192475, tag last modified 20140917 12:50:32)
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  68432 
person_id  9 
machine  Linux P4 2.8GHz 
what  prp 
notes  Command: /home/caldwell/client/pfgw f tc q"lucasU(14257,1,3779)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(14257,1,3779) [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 4673950 Running N1 test using base 3 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) 104278 bit request FFT size=(6144,17) Running N+1 test using discriminant 19, base 2+sqrt(19) 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) 104286 bit request FFT size=(6144,17) Calling N1 BLS with factored part 1.18% and helper 0.59% (4.13% proof) lucasU(14257,1,3779) is Fermat and Lucas PRP! (214.5538s+0.0050s)

modified  20040304 09:24:08 
created  20040119 11:32:51 
id  73378 

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