Yes.

> In fact, according to the celebrated prime number theorem, the number of primes less than or equal to n is asymptotic to n/log n, which means the density of primes near n is asymptotic to 1/log n.

When written down as a string of digits, log n is another way to say 'proportional to the number of digits'.

The number of digits grows fairly slowly, thus also the 'probability' of a number being prime drops very slowly.