The Prime Hunter

The question mentions 'prime,' 'prime factor,' or imposes constraints like 'p is prime and p − n = 4.' Sometimes hidden inside a probability or counting question.

Forgetting that 2 is the only even prime. Forgetting 1 is NOT prime. Forgetting the small primes (2, 3, 5, 7, 11, 13). Confusing 'prime factor' with 'prime number of factors.'

1. Have all primes under 50 memorized cold: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
2. Translate the constraint into a search over this small set.
3. Test each prime systematically against the conditions.
4. Use parity as a filter: if p + q is odd, one of them must be 2.
5. For 'prime factorization' questions: break the number down to its prime factors first, then reason.

Primes show up in roughly 10% of hard GRE questions. Knowing the small primes cold turns 90-second questions into 20-second ones.