
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
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:  103040!  1 
Verification status (*):  Proven 
Official Comment:  Factorial 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p301 : Winskill1, Fpsieve, PrimeGrid, OpenPFGW 
Decimal Digits:  471794 (log_{10} is 471793.32496352) 
Rank (*):  1730 (digit rank is 1) 
Entrance Rank (*):  136 
Currently on list? (*):  short 
Submitted:  12/14/2010 21:31:36 CDT 
Last modified:  12/18/2010 17:20:21 CDT 
Database id:  96944 
Status Flags:  none 
Score (*):  44.3267 (normalized score 1.8186) 

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 4
Subcategory: "Factorial"
(archival tag id 213027, tag last modified 20130904 05:50:30)
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.
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  20111227 16:48:35 
created  20101214 21:35:02 
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, BrillhartLehmerSelfridge] 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 BrillhartLehmerSelfridge with factored part 33.98% 103040!1 is prime! (328910.6907s+2.6303s) [Elapsed time: 3.81 days]

modified  20110118 10:15:30 
created  20101214 21:38:02 
id  123279 

Query times: 0.0005 seconds to select prime, 0.0004 seconds to seek comments.
