Displaying 1-10 of 17 results found.
719, 5702399, 889574399, 50812489727999, 17377871486975999, 3693145248412139519999, 1263108856248528850649087999999, 1174691236311131831103651839999999, 1966250441603763578045139940225843199999999
COMMENTS
Not an integer for n < 4.
MATHEMATICA
Table[(Prime[n]! - 7)/7, {n, 4, 20}]
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.
Natural numbers of the form (prime(n)!-3)/3.
+0
19
1, 39, 1679, 13305599, 2075673599, 118562476031999, 40548366802943999, 8617338912961658879999, 2947253997913233984847871999999, 2740946218059307605908520959999999, 4587917697075448348771993193860300799999999, 11150842204387935702723354017813583888383999999999, 20138421021124611879118377356171332502421503999999999, 86207747170389393547654785051203993323065877463039999999999, 1424961094686675188099337917796466549896781262788937908223999999999999
MATHEMATICA
Table[(Prime[n]! - 3)/3, {n, 2, 20}]
Natural numbers of the form (prime(n)!-6)/6.
+0
18
0, 19, 839, 6652799, 1037836799, 59281238015999, 20274183401471999, 4308669456480829439999, 1473626998956616992423935999999, 1370473109029653802954260479999999
MATHEMATICA
Table[(Prime[n]! - 6)/6, {n, 2, 20}]
0, 2, 59, 2519, 19958399, 3113510399, 177843714047999, 60822550204415999, 12926008369442488319999, 4420880996869850977271807999999, 4111419327088961408862781439999999, 6881876545613172523157989790790451199999999, 16726263306581903554085031026720375832575999999999, 30207631531686917818677566034256998753632255999999999, 129311620755584090321482177576805989984598816194559999999999, 2137441642030012782149006876694699824845171894183406862335999999999999
MATHEMATICA
Table[(Prime[n]! - 2)/2, {n, 1, 20}]
Natural numbers of the form (prime(n)! - 5)/5.
+0
18
23, 1007, 7983359, 1245404159, 71137485619199, 24329020081766399, 5170403347776995327999, 1768352398747940390908723199999, 1644567730835584563545112575999999
MATHEMATICA
Table[(Prime[n]! - 5)/5, {n, 3, 20}]
Numbers k such that (k!-4)/4 is prime.
+0
20
4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041
COMMENTS
Numbers k such that (k!-m)/m is prime:
for m=2 prime or pseudoprime see A082671
MATHEMATICA
a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; 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!-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!-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!-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).
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