My take is that a random number is far from a round one, much closer to a prime one.

As a last digit:

0, 2, 4, 6 and 8 are even, so they're out.

5 is out since it makes the number divisible by 5; a semi-even number

1 and 9 are closer to an even number so it would seem fake to choose "49" or "51" just to avoid "50"

So we're left with 3 and 7.

Similar logic, for the first letter, albeit less pronounced.

So we have 33, 37, 73 and 77.

33 and 77 are "obviously" not random so it's either 37 or 73. Not using common digits, not near the beginning, middle or end. In fact, they're closer to 25 and 75 (1/4 and 3/4 of the range) than to 0, 1/2 or 1. Also closer to 1/3 and 2/3. Just random thoughts.