26951! + 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:	26951! + 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Proof-code(s): (*):	p65 : DavisK, Kuosa, OpenPFGW
Decimal Digits:	107707 (log₁₀ is 107706.36749689)
Rank (*):	47626 (digit rank is 1)
Entrance Rank (*):	73
Currently on list? (*):	yes
Submitted:	5/23/2002 00:28:39 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	106
Status Flags:	none
Score (*):	39.7829 (normalized score 0.0047)

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 11
Subcategory: "Factorial"
(archival tag id 187620, tag last modified 2023-03-11 15:53:59)

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 106

person_id 9

machine WinXP P4 1.8GHz

what prime

notes PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 26959 Primality testing 26951!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 26981 Calling Brillhart-Lehmer-Selfridge with factored part 34.11% 26951!+1 is prime! (9769.865000 seconds)

modified 2003-03-25 17:21:47

created 2003-01-23 06:44:20

id 67338

field	value
prime_id	106
person_id	9
machine	WinXP P4 1.8GHz
what	prime
notes	PFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 26959 Primality testing 26951!+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 26981 Calling Brillhart-Lehmer-Selfridge with factored part 34.11% 26951!+1 is prime! (9769.865000 seconds)
modified	2003-03-25 17:21:47
created	2003-01-23 06:44:20
id	67338

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.