A089298 Smallest prime with digit product 10^n.

11, 251, 14551, 155581, 4545551, 45555581, 555555881, 44555555581, 455555558581, 5555555888551, 255555555585881, 14555555558558851, 155555555858885551, 2555555555558885851, 45555555555585855881

Offset: 0

Author

Amarnath Murthy, Oct 30 2003

Keywords

• base
• nonn

Comments

These numbers may not contain the digits {0, 3, 6, 7 or 9} and must end with the digit 1. Also the number of 2's plus half the number of 4's plus a quarter of the number of 8's must equal the number of 5's which in turn must equal n. - Robert G. Wilson v, Nov 06 2003

Examples

			a(4) = 4545551 and the digit product = 10^4.
		

Crossrefs

Cf. A089365, A088653, A090840, A091465, A090841.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {10}]; p = 2; Do[ q = Log[10, Times @@ IntegerDigits[p]]; If[q != 0 && IntegerQ[q] && a[[q]] == 0, a[[q]] = p; Print[q, " = ", p]]; p = NextPrim[p], {n, 1, 10^9}]; a

Extensions

Edited, corrected and extended by Robert G. Wilson v, Nov 06 2003