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 Find my number (Posted on 2011-12-19)
My number:
1. Is a 3-digit number.
2. All its digits are prime digits.
3. A number formed by its 1st 2 digits is prime.
4. So is the number formed by its last 2 digits.
5. It is the smallest number satisfying the above conditions.

Find it.

Rem: The digits in my number do not have to be distinct.

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 No problem (spoiler) | Comment 1 of 10
I did this in my head, so it meets my criteria for difficulty 1.  Unless I am missing something, which is always possible.

a) Prime digits are 2,3,5,7

b) 2 is the smallest of these.

c) 23 is the smallest two digit prime using these digits that starts with 2.  So, problem is solved if I can just form a two digit prime starting with 3 and one of those digits.

d) Oh yes, I can, it is 37. (32, 33 and 35 are not prime)

 Posted by Steve Herman on 2011-12-19 15:05:46

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