A274678 Numbers k such that 7*10^k + 27 is prime.

1, 2, 3, 5, 7, 34, 38, 49, 51, 89, 91, 132, 227, 3662, 5019, 9729, 25437, 99944, 106553, 114577

Offset: 1

Author

Vincenzo Librandi, Jul 04 2016

Keywords

• nonn
• more

Examples

			3 is in this sequence because 7*10^3 + 27 = 7027 is prime.
4 is not in the sequence because 7*10^4 + 27 = 70027 = 239 * 293.
Initial terms and associated primes:
a(1) = 1: 97;
a(2) = 2: 727;
a(3) = 3: 7027;
a(4) = 5: 700027, etc.
		

Links

• Makoto Kamada, Search for 70w27.

Crossrefs

Cf. similar sequences listed in A274676.

Programs

Magma

[n: n in [1..800] | IsPrime(7*10^n+27)];

Mathematica

Select[Range[0, 3000], PrimeQ[7 10^# + 27] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+27), 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 + 27):
            print(k, end=", ")
        k += 1
        sevenpow10 *= 10
afind(500) # Michael S. Branicky, Dec 31 2021

Extensions

a(15)-a(16) from Michael S. Branicky, Dec 31 2021

a(17)-a(20) from Kamada data by Tyler Busby, Apr 14 2024