Stephenson Prime Number Formula

The sum of the set of all the places ratios or fractions that can be written in simpliest form from (1 to n)/(1 to n) where n is any natural number.

For example 1 has 1 place 1/1 this is the 0th prime number,1.

2 has 2 additional places 1/2, 2/1 added together with the set of 1/1 we get 3, the 2 prime number.

3 has 4 additional places 1/3, 3/1, 2/3, 3/2 added together with the 1's and 2's we get 7 the 4th prime number.

4 has 4 addition places 1/4, 4/1, 3/4, 4/3 added together we get 11 the 5th prime number.

Adding 5's together which is 8 places with that of 1,2,3,4 we get 19 the 8th prime number

Adding 6's to 19 we 23 the 9th prime number as 6 has 4 places. 

Adding 7 (1/7, 7/1, 2/7, 7/2 , 3/7, 7/3 4/7, 7/4, 5/7, 7/5 7/7,7/6) we get 12 addition places which equals 31 the 11th prime number.

With 8's we get 39 not a prime number. But adding 9's the sum we get 47 the 15th prime number.

I got all the way to 15 which ends in 131 which is the 32nd prime number.

So far for all odds from 1 to 15 the sum of ratios are prime.

See how I got 132 for 15 if my writings aren't clear.

-Andrew Joel Stephenson