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PeterisP comments on Never Leave Your Room - Less Wrong
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I ask for any integer, and determine it's value modulo 2, or modulo 3 if I have an extra option.
Sorry for intruding on an very old post, but checking 'peoplerandom' integers modulo 2 is worse than flipping a coin - when asked for a random number, people tend to choose odd numbers more often than even numbers, and prime numbers more often than non-prime numbers.
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The second is also implied by the first, if "primes more often than non-primes" means "out of proportion with how many primes there are" rather than "more than 50% of the time", and I think it would be equally interesting to look at whether [odd] primes are more likely to be chosen than odd non-primes.
I wonder if the real issue is "that the person can/can't recall (part of) the factorization offhand" - that would make sense if people avoid numbers that "feel round" - something with an obscure factorization like 51 [3*17] might be more likely to be chosen than even numbers, multiples of 11, numbers that appear on a multiplication table (so, 3 times numbers 10 or less).