## Wednesday, June 01, 2005

### A New Prime Number Theory Based On Nine

A Prime is a whole number that can only be divided evenly without leaving a remainder by itself and 1. The common method of finding a Prime Number is to divide a suspected Prime Number by every number that precedes it to see if the only answer without a remainder is 1 or the chosen number. If we ignore the single digit Prime Numbers 1, 2, 3, 5, 7 you will see the Prime Numbers greater than 1 digit such as 11, 13, 17, 19 etc. will end in 1, 3, 7, and 9. Of course, other numbers that aren’t Prime Numbers also end in 1, 3, 7, 9 such as 21, 93, 57, and 49. At least it’s a start in cutting down our workload to find Primes since Primes have a high likelihood of having a unit’s digit of 1, 3, 7, 9. We can refine our technique by multiplying any whole number by 9. For instance ( 2 X 9) is 18. 18 isn’t a Prime but there is a possibility that 18 is relatively close to a Prime Number that has a unit digit of 1, 3, 7, 9. Experience will show that adding or subtracting 3 or 6 will not produce a Prime Number. ( 2 X 9 = 18 ), (18 + 6 =24 ), (18 - 6 = 12), (18 + 3 = 21), (18 - 3 = 15 ). Prime Numbers can be perhaps produced by adding 1, 2, 4, 5, 7, 8 to ( 2 X 9 = 18) or subtracting 1, 2, 4, 5, 7, 8 from ( 2 X 9 = 18) providing the resulting answer has a unit’s digit is 1, 3, 7 or 9. For Example adding 1 to (2 X 9 = 18) produces 19 and subtracting 1 from (2 X 9 = 18) produces 17 which are both Prime Numbers. Adding 5 and subtracting 5 from ( 2 X 9 = 18 )produces 13 and 23 which are both Prime Numbers. The last Prime Number associated with ( 2 X 9 = 18) is 11 by subtracting 7 from 18 (18 - 7 = 11). You will also see from the above example that you can add or subtract the same number to produce primes (2 X 9 + 5 = 23), ( 2 X 9 - 5 = 13). Shades of Ramanujan. I don’t know why it works, but it does!!!!!