409 is an interesting prime number. If you remove any number of its digits, then you will get a number that is not prime.

4=2^2
0=not prime
9=3^2
40=2^3*5
49=7^2
09=9=3^2

Call a number with this property a minimal prime. Find all minimal primes.

In recreational number theory, a minimal prime is a prime number for which there is no shorter subsequence of its digits in a given base that form a prime. In base 10 there are exactly 26 minimal primes:

<DL> <DD>2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 (sequence A071062 in OEIS).</DD></DL>

Posted by Ady TZIDON on 2012-04-24 10:37:58