"'css_descramble.c.gz' · 65536 + 2083"
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The Largest Known Primes Icon
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:"'css_descramble.c.gz' · 65536 + 2083"
Verification status (*):PRP
Official Comment:Illegal prime, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c5 : Carmody, Primo
Decimal Digits:1401   (log10 is 1400.6863241)
Rank (*):99013 (digit rank is 4)
Entrance Rank (*):33954
Currently on list? (*):no
Submitted:3/14/2001 00:17:41 CDT
Last modified:3/14/2001 00:17:41 CDT
Database id:40353
Blob database id:10
Status Flags:Verify
Score (*):26.3254 (normalized score 0)

Description: (from blob table id=10)

The first illegal prime.

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.
Illegal prime (tolerated *)
Prime on list: no, rank 2
Subcategory: "Illegal prime"
(archival tag id 176773, tag last modified 2003-11-01 21:20:04)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 848
Subcategory: "ECPP"
(archival tag id 176772, tag last modified 2019-02-16 16:50:05)

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.

Phil Carmody writes (11 Sep 2014): 

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.
machineLinux PII 200
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing 4856507896...0880529443 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N-1 BLS with factored part 0.62% and helper 0.41% (2.32% proof) 4856507896...0880529443 is Fermat and Lucas PRP! (15.650000 seconds)
modified2003-03-25 11:21:44
created2003-01-30 17:37:57

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.