Puzzle for 27 Jun 2009

Get a smallest three digit prime number which has

1. All prime digits
2. Forms a prime number with its sum of first two digits.
3. Forms a prime number with its sum of last two digits.

I think the smallest one is 523.

EDIT :: The reason is :
We have only 4 prime digits : 2, 3, 5 and 7.
We can have 4C2 = 6 different combinations, taking 2 at a time.
Out of these 6, only 2 have prime sums. They are 2,3 and 2,5.
So, the number will be 325 or 523 as 2 should be common to 3 and 5.
So, obviously 523 is the answer.

Correct and also I have a bit different logic.

2 Needs to be at middle because adding two odd number would always be even and so unprime
So now we have
_2_
Now we have 3 which can be at last place because
2 and 5 would make the number unprime
7 would make the sum unprime
_23
Now
and 3, 5 at first place are the only option
and so 323 is not a prime number.

I added smallest just to add confusion but the solution is unique.

I knew that