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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10, Math Kangaroo 5-6.

Which of the following statements is sometimes true?

The only even prime number is 2. All the other primes are odd. By adding an odd number to 2 we obtain an odd number, which can be prime. This statement can be true if one of the primes is 2.

By multiplying two primes we always get a composite number.

By subtracting 1 from a perfect square we obtain:


which has two factors and is therefore never prime.

By raising a prime to a power we always obtain a composite number.

A prime cannot be a perfect square since a perfect square has an even number of factors. Note that 1 is not a prime number.