Displaying 11-17 of 17 results found.
Numbers k such that (k!-5)/5 is prime.
+0
3
5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702, 4509, 7498
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 5)/5], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)
PROG
(Magma) [n: n in [5..500] | IsPrime((Factorial(n)-5) div 5)]; // Vincenzo Librandi, Nov 21 2016
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Numbers k such that (k!-6)/6 is prime.
+0
3
4, 5, 7, 8, 11, 14, 16, 17, 18, 20, 43, 50, 55, 59, 171, 461, 859, 2830, 3818, 5421, 5593, 10118, 10880, 24350
MAPLE
a:=proc(n) if isprime((1/6)*factorial(n)-1)=true then n else end if end proc: seq(a(n), n=4..500); # Emeric Deutsch, Apr 29 2008
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 6)/6], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1 <= m <= 10).
Numbers k such that (k!-7)/7 is prime.
+0
3
7, 9, 20, 23, 46, 54, 57, 71, 85, 387, 396, 606, 1121, 2484, 6786, 9321, 11881, 18372
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 7)/7], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
EXTENSIONS
More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
Numbers k such that (k!-8)/8 is prime.
+0
3
4, 6, 8, 10, 11, 16, 19, 47, 66, 183, 376, 507, 1081, 1204, 12111, 23181
MAPLE
a:=proc(n) if isprime((1/8)*factorial(n)-1)=true then n else end if end proc: seq(a(n), n=4..550); # Emeric Deutsch, May 07 2008
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 8)/8], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Numbers k such that (k!-9)/9 is prime.
+0
3
6, 15, 17, 18, 21, 27, 29, 30, 37, 47, 50, 64, 125, 251, 602, 611, 1184, 1468, 5570, 10679, 15798, 21237
COMMENTS
a(20) > 10000. The PFGW program has been used to certify all the terms up to a(19), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 9)/9], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a
PROG
(PARI) for(n=1, 1000, if(floor(n!/9-1)==n!/9-1, if(ispseudoprime(n!/9-1), print(n)))) \\ Derek Orr, Mar 28 2014
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Numbers k such that (k!-10)/10 is prime.
+0
20
5, 6, 7, 11, 13, 17, 28, 81, 87, 433, 640, 647, 798, 1026, 1216, 1277, 3825, 6684
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 10)/10], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)
Select[Range[700], PrimeQ[(#!-10)/10]&] (* Harvey P. Dale, Feb 15 2015 *)
CROSSREFS
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199- A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).
Smallest father factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime.
+0
2
5, 2, 2947253997913233984847871999999, 29, 23, 19, 719, 4989599, 39520825343999, 11, 11058645491711999, 419, 479001599, 359, 7, 860234568201646565394748723848806399999999
COMMENTS
For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime) see A139074. For smallest son factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime see A139206.
MATHEMATICA
a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, [(Prime[k]! - n)/n], {n, 1, 100}]; a (*Artur Jasinski*)
CROSSREFS
Cf. A139074, A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198, A136019, A136020, A136026, A136027.
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