103040! - 1

Previous Next Random

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:	103040! - 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p301 : Winskill1, Fpsieve, PrimeGrid, OpenPFGW
Decimal Digits:	471794 (log₁₀ is 471793.32496352)
Rank (*):	11345 (digit rank is 1)
Entrance Rank (*):	136
Currently on list? (*):	yes
Submitted:	12/15/2010 03:31:36 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	96944
Status Flags:	none
Score (*):	44.3267 (normalized score 0.449)

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 8
Subcategory: "Factorial"
(archival tag id 213027, 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.

PrimeGrid writes (11 Sep 2014): (report abuse)

For more information, please see the Official Announcement.

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 96944

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 103040 ! -1 2>&1 [Elapsed time: 40571.083 seconds]

modified 2020-07-07 22:30:32

created 2010-12-15 03:35:02

id 123278

field	value
prime_id	96944
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 103040 ! -1 2>&1 [Elapsed time: 40571.083 seconds]
modified	2020-07-07 22:30:32
created	2010-12-15 03:35:02
id	123278

field value

prime_id 96944

person_id 9

machine Ditto P4 P4

what prime

notes Command: /home/ditto/client/pfgw -tp -q"103040!-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 103040!-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 103043, base 1+sqrt(103043) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 3134544 bit request FFT size=(196608,16) Running N+1 test using discriminant 103043, base 2+sqrt(103043) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 3134544 bit request FFT size=(196608,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.98% 103040!-1 is prime! (328910.6907s+2.6303s) [Elapsed time: 3.81 days]

modified 2020-07-07 22:30:32

created 2010-12-15 03:38:02

id 123279

field	value
prime_id	96944
person_id	9
machine	Ditto P4 P4
what	prime
notes	Command: /home/ditto/client/pfgw -tp -q"103040!-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 103040!-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 103043, base 1+sqrt(103043) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 3134544 bit request FFT size=(196608,16) Running N+1 test using discriminant 103043, base 2+sqrt(103043) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(196608,19) to FFT(196608,18) Reduced from FFT(196608,18) to FFT(196608,17) Reduced from FFT(196608,17) to FFT(196608,16) 3134544 bit request FFT size=(196608,16) Calling Brillhart-Lehmer-Selfridge with factored part 33.98% 103040!-1 is prime! (328910.6907s+2.6303s) [Elapsed time: 3.81 days]
modified	2020-07-07 22:30:32
created	2010-12-15 03:38:02
id	123279

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