Find a 3-digit prime number consisting of 3 distinct prime digits, such that none of its other 3-digit permutations and none of its 2-digit combinations are prime?

The presence of a 2 and a 5 would aid greatly in making 2-digit subsets composite. Neither can be at the end of the 3-digit number, so try 253, 523, 257 and 527.

The ones with 3 allow for 23, a prime.

527 is not itself prime.

That leaves 257.

Any 3-digit combination that doesn't include a 2 or doesn't include a 5 will itself be divisible by 3. So the above solution is unique.

Edited on January 22, 2013, 1:46 pm

Posted by Charlie on 2013-01-22 13:41:36