Puzzle for 24 Jun 2009

Discussion in '\$1 Daily Competition' started by shabbir, Jun 24, 2009.

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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

2. SaswatPadhi~ Б0ЯИ Τ0 С0δЭ ~

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

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

3. MridulaNew Member

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4. MridulaNew Member

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5. MridulaNew Member

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

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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.

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

8. nimeshNew Member

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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.

So... now what???

What say Saswat??

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

10. SaswatPadhi~ Б0ЯИ Τ0 С0δЭ ~

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:iagree:

@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 ?!? :crazy:

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".

Last edited: Jun 24, 2009