I wouldn't call that argument my only reason, but it's my best shot at expressing my main reason in words.

Funny story: when I was typing this post, I almost typed, "If a number is not prime, it must have a prime factor greater than its square root." But that's wrong, counterexamples include pi, i, and integers less than 2. Not that I was confused about that, my real reasoning was partly nonverbal and included things like "I'm restricting myself to the domain of integers greater than 1" as unstated assumptions. And I didn't actually have to spell out for myself the reasoning why 2 and 5 aren't factors of 53; that's the sort of thing I'm used to just seeing at a glance.

This left me fearing that someone would point out some other minor error in the argument in spite of the arguments' being essentially correct, and I'd have to respond, "Well, I said I was 99.99% sure 53 was prime, I never claimed to be 99.99% sure of that particular argument."