"39337462836420334781...(30126 other digits)...64189488844826004191"

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:"39337462836420334781...(30126 other digits)...64189488844826004191"
Verification status (*):Proven
Official Comment (*):3-Carmichael factor (3)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p44 : Broadhurst, OpenPFGW
Decimal Digits:30166   (log10 is 30165.5948063)
Rank (*):68153 (digit rank is 1)
Entrance Rank (*):7708
Currently on list? (*):no
Submitted:9/26/2003 04:34:46 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:66372
Blob database id:103
Status Flags:none
Score (*):35.8567 (normalized score 0.0001)

Description: (from blob table id=103)

3 - Carmichael factor (3)

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.
n-Carmichael factor (tolerated *)
Prime on list: no, rank 1
Subcategory: "3-Carmichael factor (3)"
(archival tag id 191216, tag last modified 2023-03-11 15:53:59)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
notes

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_id66372
person_id9
machineLinux P4 2.8GHz
whatprime
notesPFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3933746283...2905457687trial factoring to 9442151 Running N-1 test using base 3 3707947076...4826004191 [N-1/N+1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(12288,21) to FFT(12288,20) Reduced from FFT(12288,20) to FFT(12288,19) Reduced from FFT(12288,19) to FFT(12288,18) Reduced from FFT(12288,18) to FFT(12288,17) 200424 bit request FFT size=(12288,17) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(12288,21) to FFT(12288,20) Reduced from FFT(12288,20) to FFT(12288,19) Reduced from FFT(12288,19) to FFT(12288,18) Reduced from FFT(12288,18) to FFT(12288,17) 200424 bit request FFT size=(12288,17) Running N+1 test using discriminant 19, base 1+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(12288,21) to FFT(12288,20) Reduced from FFT(12288,20) to FFT(12288,19) Reduced from FFT(12288,19) to FFT(12288,18) Reduced from FFT(12288,18) to FFT(12288,17) 200432 bit request FFT size=(12288,17) Calling N-1 BLS with factored part 35.96% and helper 0.02% (107.91% proof) 3933746283...4826004191 is prime! (-1960.3873s+0.0300s)
modified2020-07-07 22:30:47
created2003-09-27 01:38:53
id71280

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