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# Prime Numbers

By May 13, 2012

A prime number is a number that is bigger than one and cannot be divided evenly by any other number except one and itself.  This article will help you find out if a number is prime or not using the following methods:  factor trees, a calculator or divisibility. However, sometimes when dealing with large numbers, you may want to use the prime number calculator.

When numbers are quite large, you may find this website showing an expanding prime number archive currently sitting on 20 billion numbers discovered and indexed.  You can use multiple search methods to find a page
based on index or the prime number in question.  A great, free service to any math enthusiast or computer science individual.

May 14, 2012 at 12:31 am
(1) JG says:

CORRECTION:

A prime number is an INTEGER that is bigger than one and cannot be divided evenly by any other number except one and itself.

May 16, 2012 at 9:14 pm
(2) Jared says:

Problem is, prime numbers aren’t introduced before the term integers. I’m a 6th grade teacher and also use the term numbers. Integers are introduced in the 7th grade. I believe the concept of prime numbers begins in the 5th and 6ths grades, long before these students are introduced to the term integers.

May 20, 2012 at 2:02 pm
(3) Michael Paul Goldenberg says:

But since primes are assumed to be positive (else unique factorization goes out the window) “integer” is the wrong term anyway. “Natural number,” “counting number” or “whole number” would be correct (even though the whole numbers include zero, zero doesn’t fit the definition and can’t be a prime number). You could say “positive integer” but that is in fact the natural or counting numbers.

So, if dealing with students who don’t know what integers are, you solve the difficulty by saying, “A prime number is a natural number p greater than 1 that has no divisors other than 1 and p itself.”

Personally, I like to stress “exactly two natural number divisors,” which seems to help some students.

Getting into why we want 1 and negative numbers not to be prime means looking at the Fundamental Theorem of Arithmetic (unique factorization of the natural numbers).

May 20, 2012 at 2:02 pm
(4) Michael Paul Goldenberg says:

But since primes are assumed to be positive (else unique factorization goes out the window) “integer” is the wrong term anyway. “Natural number,” “counting number” or “whole number” would be correct (even though the whole numbers include zero, zero doesn’t fit the definition and can’t be a prime number). You could say “positive integer” but that is in fact the natural or counting numbers.

So, if dealing with students who don’t know what integers are, you solve the difficulty by saying, “A prime number is a natural number p greater than 1 that has no divisors other than 1 and p itself.”

Personally, I like to stress “exactly two natural number divisors,” which seems to help some students.

Getting into why we want 1 and negative numbers not to be prime means looking at the Fundamental Theorem of Arithmetic (unique factorization of the natural numbers).

May 30, 2012 at 6:10 pm
(5) Jonathan says:

There is a small error under the heading Calculator Method.

“Is 57 a prime number? Yes, 19 and 3 are its factors.” should be

“Is 57 a prime number? No, 19 and 3 are its factors.”

December 12, 2012 at 2:00 am
(6) Marianne says:

There are different ways to get a prime/ composite #.

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