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Prime and Nonprime Numbers : Multiplication

Does a prime number multiplied by a prime number ever result in a prime - Why? Does a nonprime multiplied by a nonprime ever result in a prime - why? Is it possible for an extremely large prime to be expressed as a large integer raised to a very large power? Explain. Are there infinitely many natural numbers that are not prime? If so, prove it.

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A prime number (or prime integer, often simply called a "prime" for short) is a positive integer >1 that has no positive integer divisors other than 1 and itself. (More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1. (Positive integers other than 1 which are not prime are called composite ...

Solution Summary

Multiplication of prime and nonprime numbers is investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.