(61310346529 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1)/35 + 13
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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)
Proof-code(s): (*):p179 : DavisK, APTreeSieve, OpenPFGW
Decimal Digits:5132   (log10 is 5131.75741507)
Rank (*):79101 (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 152, weight 35.6128194317719
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 195110, tag last modified 2016-12-18 17:20:30)
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 2014-03-19 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.
machineWinXP Pentium M 1.7GHz
notesCommand: 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 N-1 test using base 2
Primality testing (61310346529*205881*4001#*(205881*4001#+1)+210)*(205881*4001#-1)/35+13 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Calling N-1 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:
modified2005-12-10 11:09:16
created2005-10-20 07:34:35

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.