A100459 Values of n for which the decimal number 10...090...01 is an n-digit prime.

3, 11, 143, 623

Offset: 1

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 23 2004

Keywords

• nonn
• base
• more
• hard

Comments

a(5) > 84309. - Robert Price, Apr 14 2013

The number n must be of the form 2x+3, by definition. If x is odd, the number 10...090...01 is divisible by 11. Also, if x == 2 mod 6, it is divisible by 7. Thus, it must be either 4 mod 6 or 0 mod 6. Thus, 2*(6x+4) + 3 = 12x + 11 and 2*(6x+0) + 3 = 12x + 3, implying that a(n) must be congruent to 11 mod 12 or 3 mod 12. - Derek Orr, Jul 28 2014

Examples

			10000900001 is an 11-digit prime. Thus 11 is a member of this sequence. - _Derek Orr_, Jul 27 2014
		

Crossrefs

Cf. A100028, A171553.

Programs

Mathematica

2Select[Range[1000], PrimeQ[100^# + 9 * 10^# + 1] &] + 1 (* Alonso del Arte, Jul 28 2014 *)

PARI

for(n=0,10^5,p=10^(2*n+2)+9*10^(n+1)+1;if(ispseudoprime(p),print1(2*n+3,", "))) \\ Derek Orr, Jul 27 2014