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>