A082549 Numbers k such that concatenation of first k primes, separated by zeros, is prime.

1, 9, 15, 25, 59, 444

Offset: 1

Author

Farideh Firoozbakht, May 03 2003

Keywords

• nonn
• base
• hard
• more

Comments

Let w_k = (p_1)0(p_2)0(p_3)...0(p_k), where p_i is the i-th prime. k is a term if w_k is prime.

a(7) > 2615. - Derek Orr, Aug 12 2014

a(7) > 15000. - Michael S. Branicky, May 07 2025

Examples

			a(1) = 2 is a term because the first prime by itself, p_1 = 2, is prime.
a(2) = 9 because the concatenation of the first 9 primes separated by zeros is (p_1)0(p_2)0..0(p_9) = 2030507011013017019023, which is prime.
		

Programs

Mathematica

Select[Range[450],PrimeQ[FromDigits[Flatten[IntegerDigits/@Riffle[ Prime[ Range[ #]],0]]]]&] (* Harvey P. Dale, Feb 28 2020 *)

PARI

p="";for(n=1,5000,p=concat(p,"0");p=concat(p,Str(prime(n)));if(ispseudoprime(eval(p)),print1(n,", "))) \\ Derek Orr, Aug 12 2014