Question 1

What is a prime number?

Accepted Answer

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers. The number 2 is the only even prime number.

Question 2

How do you check if a number is prime?

Accepted Answer

To check if a number n is prime, test if it's divisible by any integer from 2 to the square root of n. If no divisors are found, the number is prime. For example, to check if 29 is prime, test divisibility by 2, 3, 4, and 5 (since sqrt(29) is about 5.4). Since none divide 29 evenly, it's prime.

Question 3

What is prime factorization?

Accepted Answer

Prime factorization is expressing a number as a product of prime numbers. Every positive integer greater than 1 can be uniquely represented as a product of primes. For example, 60 = 2^2 x 3 x 5. This is also called the Fundamental Theorem of Arithmetic.

Question 4

How many prime numbers are there?

Accepted Answer

There are infinitely many prime numbers. This was first proven by the ancient Greek mathematician Euclid around 300 BCE. As numbers get larger, primes become less frequent, but they never stop appearing. The largest known prime as of 2024 has over 24 million digits.

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