## Friday, December 08, 2006

### Primes

There’re a lot of things in this world that drive people nuts, but for mathematicians or the mathematically curious it seems to be Primes. Primes are defined as any number that can only be divided evenly by itself and 1. If you suspect that a number is a Prime, the only way to absolutely know if it is a Prime number is to divide it by all the preceding numbers to see if that particular number is a Prime or in other words divisible only by itself and 1. Fine for low numbers but a royal pain for large numbers. To add to the fun, if you look at a table of Primes it seems to follow a pattern, but nobody has been able to find the formula for that pattern. If you examine a table of Primes you will find that none of the Primes are an even number. Therefore if you write down all the numbers from 1 to infinity and divide the numbers by 2, and eliminate those divisible evenly by 2 it’s a start. If you look at a table of Prime Numbers you will see after the first column of Prime Numbers (1, 2, 3, 5, 7 ) the Prime Numbers with more than 1 column ( 11, 13, 17, 19 ) end in 1, 3, 7, and 9. The downside of numbers ending in 1, 3, 7 and 9 is that not all these numbers are Prime. Oh well, it’s a start for eliminating a lot of odd numbers ending in 5 that aren’t Prime. If however, you divide all the Prime numbers from 1 to infinity ending in 1, 3, 7, 9 by 9 you will find that the decimal part of the answer after dividing by 9 is .111111, .22222, .444444, .555555, .77777, .888888. You will notice that there is no .3333333 or .6666666. It seems that a odd number ending in 1, 3, 7, 9 when divided by 9 and has a decimal part of the answer being .333333 or .66666 is not a Prime number. Try it and see!!!!

In summary:

Prime numbers end in 1, 3, 7, 9 after the first column.

Not all numbers ending in 1, 3, 7, 9 are Prime numbers.

Divide all the numbers ending in 1, 3, 7, 9 by 9.

If the answer contains .33333 or .666666 or .6666667 they aren’t a Prime number.

If the answer contains .111111, .222222, .44444, .55555, .777777, or .88888 it is a Prime number.