## Friday, October 29, 2004

### How Many Prime Numbers ????

I got to thinking about prime numbers the other day. A prime number is any number that can only be divided evenly by itself and 1. For example the numbers 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 are all examples of prime numbers because they can only be divided evenly by 1 and themselves. If you look at the first digit in column 1 of any prime number you will see it will only contain the numbers 1, 3, 7, 9. The other numbers in the columns after the first column will have 10 choices of digits from 0 to 9 (0,1,2,3,4,5,6,7,8,9). Take any random number and add 1,3,7,9 to it. The new number is probably a prime. Divide it by all the preceding numbers to see if it is a prime. Therefore in a 10’s based number system the number of available digits to put in a column is 10 numbers. Since the prime numbers end in 1,3,7,9 which are 4 numbers out of the available 10 digits then the number of prime numbers is about 4/10 of the total numbers or approximately 40%. Unfortunately numbers ending in 9 are not always primes (39 for example) but the numbers 1,3,7 are always primes. Since the prime numbers ending in 1,3,7 are 3 numbers out of the available 10 digits then the number of definite prime numbers are about 3/10 of the total numbers or approximately 30%. Therefore the number of prime numbers are between 30% to 40% of all the integer numbers (1, 30, 40 etc.).