A075902 Primes p = prime(k) such that the decimal representation of p contains k as a substring.

17, 64553, 64567, 64577, 64591, 64601, 64661, 99551, 4303027, 6440999, 14968819, 95517973, 527737957, 1893230839, 1966640443, 1246492090901

Offset: 1

Author

Zak Seidov, Sep 27 2002

Keywords

• more
• base
• nonn

Comments

prime(k) = 1966640443 for k=96664044. This is the first case in which k is an internal string of prime(k). - Carlos Rivera, Jun 16 2004

2*10^12 < a(17) <= 12426836115943. a(18) <= 21732382677641. a(19) <= 154895576080181. - Donovan Johnson, May 08 2010

Examples

			Pairs {n, prime(n)}: {7, 17}, {6455, 64553}, {6456, 64567}, {6457, 64577}, {6459, 64591}, {6460, 64601}, {6466, 64661}, {9551, 99551}, {303027, 4303027}, {440999, 6440999}, {968819, 14968819}, {5517973, 95517973}.
		

Crossrefs

Cf. A067248, A046883, A075902.

Programs

Mathematica

Prime[Select[Range[10^6], StringContainsQ[ToString[Prime[#]], ToString[#]] & ]] (* Robert Price, May 27 2019 *)

Python

from sympy import primerange
[print(i,end=', ') for n,i in enumerate(primerange(1,10**7)) if str(n+1) in str(i)] # Nicholas Stefan Georgescu, Jan 03 2025

Extensions

3 more terms from Carlos Rivera, Jun 16 2004

a(16) from Donovan Johnson, May 08 2010