71509 · 2143019 - 1
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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:71509 · 2143019 - 1
Verification status (*):Proven
Official Comment:Woodall, arithmetic progression (2,d=(143018*2^83969-80047)*2^59049) [x12]
Proof-code(s): (*):g23 : Ballinger, Proth.exe
Decimal Digits:43058   (log10 is 43057.8633105718)
Rank (*):53725 (digit rank is 1)
Entrance Rank (*):23
Currently on list? (*):short
Submitted:4/25/1998 18:39:57 CDT
Last modified:4/25/1998 18:39:57 CDT
Database id:1411
Status Flags:none
Score (*):36.9557 (normalized score 0.0011)

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 46
Subcategory: "Arithmetic progression (2,d=*)"
(archival tag id 190584, tag last modified 2017-02-04 23:20:03)
Woodall Primes (archivable *)
Prime on list: yes, rank 9
Subcategory: "Woodall Primes"
(archival tag id 190583, tag last modified 2009-02-12 20:01:30)

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.
fieldvalue
prime_id1411
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 71509*2^143019-1 2>&1
Starting Lucas Lehmer Riesel prime test of 71509*2^143019-1
Using Irrational Base DWT : Mersenne fftlen = 7168, Used fftlen = 12288
V1 = 4 ; Computing U0...
V1 = 4 ; Computing U0...done.
Starting Lucas-Lehmer loop...

71509*2^143019-1 is prime! Time : 42.510 sec.
[Elapsed time: 42.00 seconds]
modified2008-05-25 22:31:34
created2008-05-25 22:09:02
id99278

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