A242564 Least prime p such that p*10^n+1, p*10^n+3, p*10^n+7 and p*10^n+9 are all prime.

19, 1657, 13, 9001, 283, 115201, 61507, 249439, 375127, 472831, 786823, 172489, 1237, 2359033, 163063, 961981, 1442017, 457, 1208833, 4845583, 1146877, 11550193, 436831, 1911031, 581047, 4504351, 215737, 3685051, 27805381, 1343791, 82491967, 15696349, 20446423

Offset: 1

Author

Derek Orr, May 17 2014

Keywords

• nonn
• hard

Examples

			2*10^3+1 (2001), 2*10^3+3 (2003), 2*10^3+7 (2007) and 2*10^3+9 (2009) are not all prime.
3*10^3+1 (3001), 3*10^3+3 (3003), 3*10^3+7 (3007) and 3*10^3+9 (3009) are not all prime.
5*10^3+1 (5001), 5*10^3+3 (5003), 5*10^3+7 (5007) and 5*10^3+9 (5009) are not all prime.
7*10^3+1 (7001), 7*10^3+3 (7003), 7*10^3+7 (7007) and 7*10^3+9 (7009) are not all prime.
11*10^3+1 (11001), 11*10^3+3 (11003), 11*10^3+7 (11007) and 11*10^3+9 (11009) are not all prime.
13*10^3+1 (13001), 13*10^3+3 (13003), 13*10^3+7 (13007) and 13*10^3+9 (13009) are all prime. Thus, a(3) = 13.
		

Crossrefs

Cf. A067267, A236042, A242562, A064281.

Programs

Mathematica

lpp[n_]:=Module[{c=10^n,p=2},While[Not[AllTrue[p*c+{1,3,7,9},PrimeQ]], p= NextPrime[ p]];p]; Array[lpp,40] (* Harvey P. Dale, Mar 24 2018 *)

Python

import sympy
from sympy import isprime
from sympy import prime
def Pr(n):
  for p in range(1,10**7):
    if isprime(prime(p)*(10**n)+1) and isprime(prime(p)*(10**n)+3) and isprime(prime(p)*(10**n)+7) and isprime(prime(p)*(10**n)+9):
      return prime(p)
n = 1
while n < 50:
  print(Pr(n))
  n += 1