3507! - 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 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:	3507! - 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	C : Caldwell, Cruncher
Decimal Digits:	10912 (log₁₀ is 10911.190551049)
Rank (*):	82795 (digit rank is 2)
Entrance Rank (*):	28
Currently on list? (*):	yes
Submitted:	10/1992
Last modified:	3/11/2023 15:54:10 UTC
Database id:	16968
Status Flags:	none
Score (*):	32.7103 (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.

Factorial primes (archivable *)
Prime on list: yes, rank 16
Subcategory: "Factorial"
(archival tag id 194146, 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.

Chris Caldwell writes (11 Sep 2014): (report abuse)

For more information see [Caldwell95].

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 16968

person_id 9

machine Windows XP P4 1.8GHz

what prime

notes Primality testing 3507!-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 33.70% 3507!-1 is prime! (177.857000 seconds) PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N+1 test using discriminant 3511, base 1+sqrt(3511)

modified 2003-03-25 17:23:45

created 2002-12-27 22:13:25

id 54242

field	value
prime_id	16968
person_id	9
machine	Windows XP P4 1.8GHz
what	prime
notes	Primality testing 3507!-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 33.70% 3507!-1 is prime! (177.857000 seconds) PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N+1 test using discriminant 3511, base 1+sqrt(3511)
modified	2003-03-25 17:23:45
created	2002-12-27 22:13:25
id	54242

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.