A213305 Minimal prime with n nonprime substrings (Version 1: substrings with leading zeros are considered to be nonprime).

2, 13, 11, 127, 103, 101, 1013, 1019, 1021, 1009, 10177, 10037, 10067, 10007, 10009, 100237, 100271, 100153, 100043, 100003, 100049, 1001173, 1000313, 1000037, 1000033, 1000039, 1000003, 1000081, 10000379, 10001237, 10000223

Offset: 0

Author

Hieronymus Fischer, Aug 26 2012

Keywords

• nonn
• base

Examples

			a(0) = 2, since 2 is the least prime with zero nonprime substrings.
a(1) = 13, since 13 is the least prime with exactly 1 (“1”) nonprime substrings.
a(2) = 11, since 11 is the least prime with exactly 2 (“1” and “1”) nonprime substrings.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685.

Cf. A035244, A079307, A213300 - A213321.

Formula

a(n) > 10^floor((sqrt(8*n+1)-1)/2) for n>0.

a(m(m+1)/2) > 10^m, m>0.

a(n) >= A213302(n).