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

3, 11, 143, 623

Offset

1,1

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

Links

Table of n, a(n) for n=1..4.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A100028, A171553.

Sequence in context: A329626 A072639 A201000 * A010682 A080987 A132561

Adjacent sequences: A100456 A100457 A100458 * A100460 A100461 A100462

Keyword

nonn,base,more,hard

Author

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

Status

approved