OFFSET
1,1
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Derek Orr, May 17 2014
STATUS
approved