# Minimum set of US coins to count each prime number less than 100

Say I wanted to be able to carry enough coins in my pocket such that at any time, I could count out exact change totaling any of the prime numbers less than 100. How would I determine the minimum set of coins I would need to carry? I don't care about being able to count out multiple primes - meaning the set does not have to remain useful after one number has been counted out.

So, given the standard US coins: penny, nickel, dime, and quarter - what would be the minimum number of each coin that I would need to be able to count out exactly 3, 5, 7, 11 up to 97 cents.

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Are you asking for the minimum for each prime separately, or are you asking for the minimum collection that suffices to make every prime amount less than $100$? –  Brian M. Scott May 10 '12 at 3:17