Curious Pi convergents

[Rudy Toody]

I modified Euler's Prime Product to skip the 2 and 3. Notice the square result.

I created a similar infinite product using the 6n between potential twin primes.

The second result is the square root of the first.

Any significance to this?

Note: I moved the denominators of the results to the right side of the equations to emphasize Pi.

 

[Rudy Toody]

I have spent the day searching for infinite products that produce Pi.

Only one found. It produces Pi / 2. It doesn't look like either of my products.

Maybe, I'm on to something!