A274677 Numbers k such that 7*10^k + 19 is prime.

1, 2, 3, 4, 27, 32, 63, 69, 107, 145, 154, 173, 190, 271, 412, 1219, 1509, 2392, 4444, 5567, 7424, 32174, 51573

Offset: 1

Author

Vincenzo Librandi, Jul 04 2016

Keywords

• nonn
• more

Comments

No term is divisible by 6 (A047253) because 7*1000000^k + 19 = 7*(76923*13 + 1)^k + 19 is divisible by 13 and is therefore not prime. - Bruno Berselli, Jul 05 2016

Examples

			3 is in this sequence because 7*10^3 + 19 = 7019 is prime.
5 is not in the sequence because 7*10^5 + 19 = 79*8861.
Initial terms and associated primes:
a(1) = 1: 89;
a(2) = 2: 719;
a(3) = 3: 7019;
a(4) = 4: 70019, etc.
		

Links

• Makoto Kamada, Search for 70w19.

Crossrefs

Subsequence of A047253.

Cf. similar sequences listed in A274676.

Programs

Magma

[n: n in [1..800] | IsPrime(7*10^n+19)];

Mathematica

Select[Range[0, 3000], PrimeQ[7 10^# + 19] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+19), print1(n, ", "))); \\ Altug Alkan, Jul 05 2016

Python

from sympy import isprime
def afind(limit, startk=0):
    sevenpow10 = 7*10**startk
    for k in range(startk, limit+1):
        if isprime(sevenpow10 + 19):
            print(k, end=", ")
        k += 1
        sevenpow10 *= 10
afind(500) # Michael S. Branicky, Dec 31 2021

Extensions

a(20)-a(21) from Michael S. Branicky, Dec 31 2021

a(22)-a(23) from Kamada data by Tyler Busby, Apr 14 2024