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Search: a139204 -id:a139204
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Numbers n such that (n!-2)/2 is a prime.
+10
20
3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830
OFFSET
1,1
EXAMPLE
(4!-2)/2 = 11 is a prime.
MATHEMATICA
Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* Vincenzo Librandi, Feb 18 2015 *)
PROG
(PARI) xfactpk(n, k=2) = { for(x=2, n, y = (x!-k)/k; if(isprime(y), print1(x", ")) ) }
(Magma) [n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // Vincenzo Librandi, Feb 18 2015
KEYWORD
hard,more,nonn
AUTHOR
Cino Hilliard, May 18 2003
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by T. D. Noe, Oct 30 2008
STATUS
approved
Numbers k such that (k!-4)/4 is prime.
+10
20
4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041
OFFSET
1,1
COMMENTS
Numbers k such that (k!-m)/m is prime:
for m=1 see A002982
for m=2 prime or pseudoprime see A082671
for m=3 see A139056
for m=4 see A139199
for m=5 see A139200
for m=6 see A139201
for m=7 see A139202
for m=8 see A139203
for m=9 see A139204
for m=10 see A139205
a(17) > 2000 - Ray G. Opao, Sep 30 2008
a(21) > 25000 - Robert Price, Sep 25 2016
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)
PROG
(PARI) is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Artur Jasinski, Apr 11 2008
EXTENSIONS
a(15)-a(16) from Ray G. Opao, Sep 30 2008
a(17) from Serge Batalov, Feb 18 2015
a(18)-a(20) from Robert Price, Sep 25 2016
STATUS
approved
Primes of the form k! / 9 - 1.
+10
2
79, 145297151999, 39520825343999, 711374856191999, 5676771352412159999, 1209874383379816906751999999, 982417999304411328282623999999, 29472539979132339848478719999999, 1529305899025149449590664397953433599999999
OFFSET
1,1
MATHEMATICA
Select[Table[k! / 9 - 1, {k, 6, 100}], PrimeQ[#]&]
KEYWORD
nonn,changed
AUTHOR
Robert Price, Jul 19 2017
EXTENSIONS
Missing terms inserted by Alois P. Heinz, Dec 05 2024
STATUS
approved

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