Which is the smallest positive prime which is some multiple of seven less than a cube of a counting number less than 10?

Answer 1

Let's call the prime p, the multiple 7n, and the counting number c.

So:

p = c3 - 7n, p > 1, 0 < c < 10, n > 0

c can't be 1 or 2, since p and n have to be positive.

c = 3, then p = 27 - 7n

n = 2, then p = 13

So, the smallest prime that meets the conditions is 13.