Prime numbers and finite sets

The distrubution of prime numbers is interesting to me. I have found an
interesting way to study them creating the limit (p_1 x p_2 x p_3 ... x
p_n) - 1.

We can create sets that allow to find new prime numbers and remove ones
we thought were prime using our nth prime that we are using on our nth
set.
First we start with two, {0,1} We pick out 1
Second we use three, {0,1,2,3,4,5} 1 x 3 = 3, and so we remove 3 ( we
do know that 3 is prime) We also remove 0, 0 + 2, 0 + 4. We get 1 & 5.
Our new list of what think is prime is up to 2 x 3 x 5 is
{1,5,7,11,13,17,19,23,25,29}
We remove 1 x 5 and 5 x 5. Our new list is [1,7,11,13,17,19,23,29}

Remove 1 and put back the primes we used.
I hope one can see how this works.

Timothy Clemans

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