Find the smallest prime that does not divide any 5-digit number whose digits are in a strictly increasing order.

__Solution__ :

Let digit number be a 5-digit number

with

Let

Then

and

so is not divisible by 11 and hence is not divisible by 11,

Thus 11 is the smallest prime that does not divide any 5-digit number whose digits are in a strictly increasing order.

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## About benvitalis

math grad - Interest: Number theory

I recon its 11, the next one after that is 97.

here is a bit of MMA code

Paul.

Check out my post