I would say use the idea of euler's formula, x <= 1e18 would have atmax 20 primes.

Let the length of range be L, after using each of the primes to discard numbers, number of coprime numbers in range would probably be

$N = L * (1 - 1 / 2) * (1 - 1 / 3) * (1 - 1 / 5) ...$

for first 20 primes thats about $0.12L$. So for about $L >= 10$ you should expect to see atleast one coprime number.

I know this may be a totally wrong way of proving, but thats just my intution for this.