
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:  (61310346529 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001#  1)/35 + 13 
Verification status (*):  Proven 
Official Comment:  Consecutive primes arithmetic progression (3,d=6) 
Proofcode(s): (*):  p179 : DavisK, APTreeSieve, OpenPFGW 
Decimal Digits:  5132 (log_{10} is 5131.75741507) 
Rank (*):  78654 (digit rank is 16) 
Entrance Rank (*):  36952 
Currently on list? (*):  no 
Submitted:  10/19/2005 09:06:45 CDT 
Last modified:  10/20/2005 07:35:36 CDT 
Database id:  75974 
Status Flags:  none 
Score (*):  30.3699 (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.
 Arithmetic Progressions of Primes (archivable class *)
 Prime on list: no, rank 147, weight 35.6128194317719
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 195110, tag last modified 20160616 23:20:39)  Consecutive Primes in Arithmetic Progression (archivable class *)
 Prime on list: no, rank 17
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 195109, tag last modified 20140319 14:52:09)
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  75974 
person_id  9 
machine  WinXP Pentium M 1.7GHz 
what  prime 
notes  Command: pfgw.exe n f tc hhelp.txt x202746 q"(61310346529*205881*4001#*(205881*4001#+1)+210)*(205881*4001#1)/35+13" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Reading factors from helper file help.txt trial factoring to 1394925 Running N1 test using base 2 Primality testing (61310346529*205881*4001#*(205881*4001#+1)+210)*(205881*4001#1)/35+13 [N1/N+1, BrillhartLehmerSelfridge] Calling N1 BLS with factored part 33.29% and helper 0.02% (99.90% proof) (61310346529*205881*4001#*(205881*4001#+1)+210)*(205881*4001#1)/35+13 is prime! (57.3201s+0.0015s) Running N+1 test using discriminant 7, base 1+sqrt(7) [Elapsed time: 58 seconds] Helper File: 2 3 5 205881*4001#+1 205881*4001#1 
modified  20051210 11:09:16 
created  20051020 07:34:35 
id  81186 

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.
