A factorial prime is a prime number of the form factorial .
prime
for A002982 ),
the largest of which are summarized in the following table.
digits discoverer 107,707 Marchal,
Carmody, and Kuosa (Caldwell; May 2002) 142,891 Marchal, Carmody, and Kuosa (Caldwell; May 2002) 429,390 D. Domanov/PrimeGrid (Oct. 4,
2010) 471,794 J. Winskill/PrimeGrid
(Dec. 14, 2010) 700,177 PrimeGrid
(Aug. 30, 2013) 1,015,843 S. Fukui
(Jul. 25, 2016; http://primes.utm.edu/primes/page.php?id=121944 )
prime
for A002981 ; Wells 1986,
p. 70), the largest of which are summarized in the following table.
digits discoverer 107,707 K. Davis
(May 24, 2002) 507,082 PrimeGrid
(Jun. 14, 2011) 712,354 PrimeGrid
(Aug. 39, 2013)
A distributed project searching for factorial primes is being conducted on PrimeGrid.
See also Double Factorial Prime ,
Factorial ,
Integer
Sequence Primes ,
Prime Number ,
Primorial
Prime
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References Boncompagni, B. "Factorization of Special Form Numbers." http://factors.redgolpe.com/ . Borning,
A. "Some Results for Math. Comput. 26 ,
567-570, 1972. Buhler, J. P.; Crandall, R. E.; and Penk, M. A.
"Primes of the Form Math. Comput. 38 ,
639-643, 1982. Caldwell, C. K. "Prime Links++." http://primes.utm.edu/links/theory/special_forms/near_products/factorial . Caldwell,
C. K. "The Top Twenty: Factorial." http://primes.utm.edu/top20/page.php?id=30 . Caldwell,
C. K. "On the Primality of Math. Comput. 64 ,
889-890, 1995. Dubner, H. "Factorial and Primorial Primes."
J. Rec. Math. 19 , 197-203, 1987. Carmody, P. http://fatphil.org/Nuutti/ . Guy,
R. K. Unsolved
Problems in Number Theory, 2nd ed. Kuosa, N. "Factorial Prime Search Progress Pages" http://83.143.57.194:16384/Factorial/ . Pickover,
C. A. The
Mathematics of Oz: Mental Gymnastics from Beyond the Edge. PrimeGrid. "World Record
Factorial Prime!!!." http://www.primegrid.com/forum_thread.php?id=1336&nowrap=true#26809 .
Oct. 5, 2010. PrimeGrid. "PrimeGrid Primes: Subproject: (FRS)
Factorial Prime Search." http://www.primegrid.com/primes/primes.php?project=FRS . PrimeGrid
PRPNet. "Factorial Prime Search - Primes by User." http://prpnet.primegrid.com:12002/user_primes.html . PrimeGrid
PRPNet. "Factorial Prime Search - Server Statistics." http://prpnet.primegrid.com:12002 . Sloane,
N. J. A. Sequences A002981 /M0908
and A002982 /M2321 in "The On-Line Encyclopedia
of Integer Sequences." Temper, M. "On the Primality of Math. Comput. 34 ,
303-304, 1980. Wells, D. The
Penguin Dictionary of Curious and Interesting Numbers. Referenced on Wolfram|Alpha Factorial Prime
Cite this as:
Weisstein, Eric W. "Factorial Prime."
From MathWorld https://mathworld.wolfram.com/FactorialPrime.html
Subject classifications
,
where 
is a factorial.
is prime
for 
,
4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610,
6917, 21480, 26951, 34790, 94550, 103040, 147855, 208003, ... (OEIS A002982),
the largest of which are summarized in the following table.
is prime
for 
,
2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951,
110059, 150209, ... (OEIS A002981; Wells 1986,
p. 70), the largest of which are summarized in the following table.
and 
." Math. Comput. 26,
567-570, 1972.Buhler, J. P.; Crandall, R. E.; and Penk, M. A.
"Primes of the Form 
and 
." Math. Comput. 38,
639-643, 1982.Caldwell, C. K. "Prime Links++." 
and 
." Math. Comput. 64,
889-890, 1995.Dubner, H. "Factorial and Primorial Primes."
J. Rec. Math. 19, 197-203, 1987.Carmody, P. 
and 
." Math. Comput. 34,
303-304, 1980.Wells, D.