Puzzle for 24 Jun 2009

Find Smallest 3 digit prime number which has

1. All unique digits
2. All the digits are prime
3. Any combination of those digits are also prime

What does this mean : "Any combination of those digits are also prime" ??

Any 2-digit, 3-digit, 4-digit or how many digit combination ?!?

1 3 7

1 7 9

here, 197, 971, 917 all prime numbers.
Is this you meant? Hope so.

Yes.

Any combination of digits I meant

• 13
• 31
• 17
• 71
• 37
• 73
• 173
• 137

Mridula you have the right answer and its 137. I mentioned smallest and so your other answer are not valid.

BTW how did you found the answer would also be interesting to hear.

Shabbir: I would like to highlight something here.

As per the rules:
Added 19th Jun 2009 - You can post as many answers as you like, but only your last posted answer will be considered.

Mridula posted multiple answers and you said that his first reply 137 is the right answer

So... now what???

What say Saswat??

hmmmmm !!! So I guess this goes down as one more question where we have no winner.

@shabbir

Anyway, this question was INCORRECT. So, it should be canceled. (Just another reason)
137 and 173 are NOT the only 3-digit combinations of 1, 3, and 7.
Combinations like 371, 713 and 731 are composite.
And how come the digit '1' is prime ?!?

These were the errors I had noticed and so I asked you, if we had to consider 2-digit and 3-digit combinations too. And then there was a power outage here for about an hour.

Even if we were to consider only 2-digit combinations ONLY, then also such a number is impossible 'cuz 2, 3, 5, 7 are the only prime digits and if we choose any 3 out of them, we will have to select 2 or 5 or both. But then any 2-digit number of the form X2 or X5 (where X is any digit, in this case 3 or 7), is composite !

So, this question should NOT have the (invalid) 3rd requirement : "Any combination of those digits are also prime".