Prime Time

History of Prime Numbers

Primes are believed to have been first studied by the ancient Greeks. Unfortunately, after the Greeks, primes weren’t studied until the 17th century. This led to some further developments in the field. In the 19th century, the field of prime numbers changed a lot. One was denounced as a prime number, and the field advanced in leaps and bounds with the use of computers. Computers allowed mathematicians to calculate large numbers easily to determine if they are prime, which saved them a lot of trouble. Also, programs could be made that automatically generate huge prime numbers that simply couldn’t be calculated by hand.

For a while, the number one was considered prime, however, things have changed, and at this point in time one is not considered a prime number. The reasoning behind this is that the definition of a prime is a natural number that is only divisible by one and itself. The argument against the number one is that it only have one natural number factor, which is of course itself. This has been debated, and it seems to come down to a matter of opinion.

Before computers, Eratosthenes, a brilliant Greek, made up a simple method of coming up with large quantities of prime numbers. For example, lets use the numbers one to one-hundred. They are put in a grid, and then all the multiples of numbers are crossed out until you reach the square root of the largest number in the grid. If you were making a grid of 1-100, you would only have to cross out the multiples of 2, 3, 4, 5, 6, 7, 8, 9, and then finally 10. You could stop at ten because ten is the square root of 100. But, because some of these multiples are simply multiples of other numbers, we can cross out 6, 8, 9, and 10. This means that on our chart, we only have to cross out the multiple of 2, 3, 5, and 7. Once you cross out these multiples, then the numbers that remain and are not crossed out are prime. This is the easiest method of coming up with a large quantity of prime numbers, by hand. You could calculate the numbers up to 200; 1,000 or even 10,000 if you felt the need to.

The following is a blank sieve.

01, 02, 03, 04, 05, 06, 07, 08, 09, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90,
91, 92, 93, 94, 95, 96, 97, 98, 99, 100

The following is a prime number sieve with multiples of 2-10 crossed off. What is left are the prime numbers.

01, 02, 03, 04, 05, 06, 07, 08, 09, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90,
91, 92, 93, 94, 95, 96, 97, 98, 99, 100