## Tuesday, November 11, 2008

### Prime Secrets

1. Primes are defined as any number that can only be divided evenly by itself and 1.

2. Primes end in 1, 3, 7, 9 in column "0" ( far right column ).

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

4. Numbers that aren’t prime numbers but end in 1, 3, 7, 9 are evenly divisible by some number ending in 1, 3, 7, 9 in column "0" ( far right column ).

5. Except for the prime number 3, any number ending in 1, 3, 7, 9, say (39), when their digits are totaled ( 3 + 9 = 12 ) are not a prime if the total of their digits can be evenly divided by 3 ( 3 + 9 = 12) ( 12 / 3 = 4 ) ( 39 / 13 = 3 ).

6. The number of primes preceding a prime number can be approximated by first taking a prime number, say (7919), and counting all its’ digits. Prime number ( 7919 ) has 4 digits ( 7,9,1,9 = 4 digits ). The other method is to count all of the prime’s digits and subtract (1). Prime number ( 7919 ) has 4 digits and subtracting ( 1 ) leaves 3 digits. Prime number ( 7919 ) has 4 digits ( 7, 9, 1, 9 = 4 digits ), and subtracting (1) leaves ( 4 - 1 = 3 ) digits. Next take the total number of its’ digits or the total number of its’ digits minus 1 and multiple the prime ((7919) X (½ ^ 4) = 494.94) or ((7919) X (½ ^ 3) = 989.88). Since it’s unlikely that 7919 only has approximately 494 primes behind it, the likelier answer is around 989. Add 2, 4, 6, 8, 10 to 989 to get a closer approximate number. In this case add 10. ( 989.88 + 10 = 999.88 ). 7919 is the 1000th prime according to the tables. The approximation requires some obvious juggling but if you apply points 1 to 5 to the approximation you will come close to a probable answer.