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 onehundred. 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 1100, 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 210 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
