This is really obvious. All two digits composite numbers must have a factor less than or equal to their square root. Square root of 100 is 10. Thus all composite numbers under 100 must have a factor under 10. There are only four primes less than 10: 2, 3, 5 and 7.

Once you exclude all numbers divisible by 2, 3 and 5 these are the composite numbers left: 49, 77, 91.

Looks like there's a missing space after 91. That makes 91.49 look like a decimal, rather than the start of another sentence.

Kiitos, will rm in the morning

I've heard this as 91 is the smallest (or only two-digit) composite number that "looks prime".

That's a really good way to put it, it's the only one I might reliably trip up on.