The squares of primes become memorable if you've ever tried searching for primes in your head. That's because 7*7 is the smallest product of prime factors that

The squares of primes become memorable if you've ever tried searching for primes in your head. That's because 7*7 is the smallest product of prime factors that are all larger than or equal to 7: in other words, you can check for the primality of numbers smaller than that by testing for division by 2, 3, or 5 only, because they must divide by one of those or be prime. Because of this pointless mental exercise it also sticks in my mind that 11 squared is 121 and 13 squared is 169 (though the presence of 69 helps with that one).