As you can see, the word “prime" has many uses and meanings. When referring to numbers, though, prime has a special definition. A prime number is a whole number greater than 1 that can only be divided equally by itself and 1. In other words, prime numbers have only themselves and 1 as factors.
Any number may be made by multiplying two or more other numbers together. The numbers you multiply together are called factors of the final number. For prime numbers, their only factors are themselves and 1.
Let's take a look at the numbers 1 through 10 as examples:
- 1: not a prime number by definition
- 2: can only be divided by 2 and 1, so 2 is prime
- 3: can only be divided by 3 and 1, so 3 is prime
- 4: can be divided by 4, 2 and 1, so 4 is not prime
- 5: can only be divided by 5 and 1, so 5 is prime
- 6: can be divided by 6, 3, 2 and 1, so 6 is not prime
- 7: can only be divided by 7 and 1, so 7 is prime
- 8: can be divided by 8, 4, 2 and 1, so 8 is not prime
- 9: can be divided by 9, 3 and 1, so 9 is not prime
- 10: can be divided by 10, 5, 2 and 1, so 10 is not prime
Numbers that are not prime numbers are called composite numbers. You may have noticed that every even number greater than 2 is a composite number. This is because every even number greater than 2 is divisible by 2, so they cannot be primes. Thus, 2 is the only even prime number!
Here is a list of the 25 prime numbers between 1 and 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Although some experts believe that the ancient Egyptians knew about prime numbers, it was the ancient Greeks who first studied prime numbers in depth. In fact, it was Greek mathematician Euclid who proved that an infinite number of prime numbers exists. So that list of prime numbers above just keeps going and going…
Mathematicians consider prime numbers to be the “building blocks" of all numbers. According to the fundamental theorem of arithmetic, every positive whole number greater than 1 can be written as a unique product of one or more prime numbers.
If you're wondering about the largest prime number found to date, it's pretty big! In 2008, a group of people used the combined computing power of hundreds of computers to discover a prime number that has approximately 13 million digits!