I came across a problem that required finding the first 10 numbers (n > 2) with the following property:
all positive numbers x less than n that have GCD(x, n) = 1 should be prime
example:
12 is such a number because all x that have GCD(x, 12) = 1 are prime (those being 5, 7 and 11)
15 isn't such a number because GCD(4, 15) = 1 for instance, but 4 isn't a prime number
I wrote a simple program that tries to look after such numbers, the first eight being:
3, 4, 6, 8, 12, 18, 24 and 30 being the last found (either because the next one is a really big number or because there isn't another one).
So my guess right now is that there aren't more than 8, which brings me to my question. Is there a way you can prove there aren't more than 8 using math? (or work some sort of logic that tries to find out how big would the next one be if there is)