The sequence for Z! is as follows

1!=1

2!=1*2=2

3!=1*2*3=6

4!=1*2*3*4=24

5!=1*2*3*4*5=120

Z[!P] follows the exact same sequence as Z! except that it skips non-

primes as follows

2[!P]=2

3[!P]=2*3=6

5[!P]=2*3*5=30

7[!P]=2*3*5*7=210

11[!P]=2*3*5*7*11=2310

Guess what the "magic" numbers are? They are as follows: 2, 6, 30,

210, 2310, 30030, 510510, 9699690 etcetera.

2 is a magic number because every prime except 2 is a multiple of 2

plus or minus 1

6 is a magic number because every prime except 2 and 3 is a multiple

of 6 plus or minus 1

It gets more complicated after that but every set of twin primes

except 3, 5 and 7 are multiples of 30 plus or minus 1, 11, or 13

Do you see why these are "magic" numbers.

The reason why my process takes so much time to calculate the 2 is

prime is because 2 is the only prime between 1 and the first magic

number which is 2. It takes an equal amount of time to calculate the

primes between 2 and the next magic number 6, therefore 3 and 5 are

found in the same amount of time it takes to find 2. The next set of

primes found as a set using my process is all the primes between 6

and the next magic number which is 30. (I mistakenly said in a

previous post that this set included 31. 31 is actually part of the

set between 30 and the next magic number 210.)

This process finds all the primes between one magic number and

another magic number.