
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
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:  (1549^{12973}  1)/1548 
Verification status (*):  PRP 
Official Comment:  Generalized repunit 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p170 : Wu_T, Primo, OpenPFGW 
Decimal Digits:  41382 (log_{10} is 41381.347271634) 
Rank (*):  52091 (digit rank is 1) 
Entrance Rank (*):  31493 
Currently on list? (*):  short 
Submitted:  12/12/2010 12:55:04 CDT 
Last modified:  12/12/2010 13:50:21 CDT 
Database id:  96872 
Status Flags:  Verify 
Score (*):  36.8331 (normalized score 0.001) 

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.
 Generalized Repunit (archivable *)
 Prime on list: yes, rank 11
Subcategory: "Generalized Repunit"
(archival tag id 213016, tag last modified 20151101 01:50:33)
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  96872 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/pfgw o f q"(1549^129731)/1548" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 13257035 (1549^129731)/1548 has no small factor. [Elapsed time: 44.319 seconds]

modified  20111227 16:48:35 
created  20101212 13:05:06 
id  123133 

field  value 
prime_id  96872 
person_id  9 
machine  Ditto P4 P4 
what  prp 
notes  Command: /home/ditto/client/pfgw tc q"(1549^129731)/1548" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (1549^129731)/1548 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(16384,20) to FFT(16384,19) Reduced from FFT(16384,19) to FFT(16384,18) Reduced from FFT(16384,18) to FFT(16384,17) 274940 bit request FFT size=(16384,17) Running N+1 test using discriminant 17, base 3+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(16384,20) to FFT(16384,19) Reduced from FFT(16384,19) to FFT(16384,18) Reduced from FFT(16384,18) to FFT(16384,17) 274948 bit request FFT size=(16384,17) Calling N1 BLS with factored part 0.25% and helper 0.02% (0.79% proof) (1549^129731)/1548 is Fermat and Lucas PRP! (764.8700s+0.0100s) [Elapsed time: 12.80 minutes]

modified  20110118 10:15:30 
created  20101212 13:09:19 
id  123135 

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