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Q: What square numbers below 100 are also prime numbers?

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Square numbers can't be prime. They have too many factors.

Absolutely not. A square number has an integer square root, so by definition it has at least one factor. Prime numbers have no factors

i would say no

Every square number (except 1) is composite. Prime numbers only have two factors, one and the numbers themselves. Since square numbers also have at least the square roots as factors, they have to be composite.

No, square numbers greater than 1 have more than two factors.

I might be reading this incorrectly, but it seems to me that I can take two prime numbers, 3 and 3, and make the square number nine out of them. This is also true of all the other prime numbers.

No. That isn't possible: A prime number, by definition, has no smaller factors. A square number does have a smaller factor - the number that is squared.

Square numbers, greater than 1, have more than two factors.

You don't. All prime numbers are also whole numbers.

There are no other prime numbers that are even but 2.

The set of prime factors of the numbers from 1 to 15,000 would be the set of prime numbers between 1 and 15,000. The link below has a list of the first 10,000 prime numbers, so if you take the primes less than 15,000, you will have the set of prime factors of the first 15,000 numbers. For prime factors of individual numbers, check the related question, "What are the prime factors of the numbers from 1 to 200?" Also check for WikiAnswers questions in the form of "What are the prime factors of __?" and "What are the factors and prime factors of __?"

This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.

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