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Numbers k such that 2*k! - 1 is prime.
+10
11
2, 3, 4, 5, 6, 7, 14, 15, 17, 22, 28, 91, 253, 257, 298, 659, 832, 866, 1849, 2495, 2716, 2773, 2831, 3364, 5264, 7429, 28539, 32123, 37868
EXAMPLE
k = 5 is here because 2*5! - 1 = 239 is prime.
PROG
(Magma) [n: n in [1..600] | IsPrime(2*Factorial(n)-1)]; // Vincenzo Librandi, Feb 20 2015 (PARI) is(k) = ispseudoprime(2*k!-1); \\ Jinyuan Wang, Feb 04 2020
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002
Numbers k such that 3*k! - 1 is prime.
+10
11
0, 1, 2, 3, 4, 5, 9, 12, 17, 26, 76, 379, 438, 1695, 6709, 13313, 18504, 19021, 24488, 45552, 49085
EXAMPLE
k = 5 is here because 3*5! - 1 = 359 is prime.
MAPLE
for n from 0 to 1000 do if isprime(3*n! - 1) then print(n) end if end do;
MATHEMATICA
Select[Range[0, 10^3], PrimeQ[3 #! - 1] &] (* Robert Price, May 27 2019 *)
PROG
(PARI) isok(n) = isprime(3*n! - 1); \\ Michel Marcus, Nov 13 2016 (PFGW) ABC2 3*$a!+1
AUTHOR
Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002
Numbers k such that 4*k! - 1 is prime.
+10
11
0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843
EXAMPLE
k = 5 is here because 4*5! - 1 = 479 is prime.
MAPLE
for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;
Numbers k such that 5*k! - 1 is prime.
+10
10
3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080
EXAMPLE
k = 5 is here because 5*5! - 1 = 599 is prime.
MAPLE
for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;
PROG
(Python)
from sympy import isprime
from math import factorial
print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021
Numbers k such that 6*k! - 1 is prime.
+10
10
0, 1, 2, 5, 8, 42, 318, 326, 1054, 2987, 11243
MATHEMATICA
fQ[n_] := PrimeQ[6 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
PROG
(PARI) is(k) = ispseudoprime(6*k!-1); \\ Jinyuan Wang, Feb 04 2020
Numbers k such that 10*k! - 1 is prime.
+10
10
2, 3, 4, 33, 55, 95, 110, 148, 170, 612, 1155, 2295, 2473, 4143, 5671
MATHEMATICA
fQ[n_] := PrimeQ[10 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
Numbers k such that 9*k! - 1 is prime.
+10
8
2, 3, 12, 15, 16, 25, 30, 38, 59, 82, 114, 168, 172, 175, 213, 229, 251, 302, 311, 554, 2538, 3050, 3363, 12316
MATHEMATICA
fQ[n_] := PrimeQ[9 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
PROG
(PARI) is(k) = ispseudoprime(9*k!-1); \\ Jinyuan Wang, Feb 03 2020
Numbers k such that 8*k! - 1 is prime.
+10
6
0, 1, 3, 4, 8, 33, 121, 177, 190, 276, 473, 484, 924, 937, 1722, 2626, 4077, 4464, 6166
MATHEMATICA
fQ[n_] := PrimeQ[8 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
PROG
(PARI) is(k) = ispseudoprime(8*k!-1); \\ Jinyuan Wang, Feb 03 2020
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