People think even numbers aren't as "random" and odd numbers are more "random". That leaves us with 1,3,5,7,9. 1 and 5 both divide 10 and don't seem so "random" to us, I guess. That leaves us with 3, 7, and 9. 33, 77, 99, i.e. numbers with repeated digits don't seem so "random". That leaves us with 37, 39, 79. And 9 maybe (not sure if all people subconsciously think this way) isn't that "random" because it's one less than 10 and divisible by 3.

Infact, the jargon file says that 37 is the most common random number people will choose[0].

[0] http://catb.org/jargon/html/R/random-numbers.html

23,29,31,37,41,43,47,53,59,61,67,71 73,79,83,89,97

Evens are out; so are small multiples. A multiple of three might end in 3, 9 or 7. A multiple of 7 may end in 1. So a "conservative mental arithmetic sieve" that wants to make sure one's picking a prime number will coalesce around 29 or 37.

Myself, I picked 11 and 17.

I saw a list once of what makes each number from 1 to 100 special. One of them was the most random number (I think 37). Another one was the least special (63 perhaps?).