Need Help with Triplet Theory of...

[googol]

Primes.

I need to find series of 3 prime numbers that are in the form of

P+0(16), P+1(16), P+2(16).

The numbers can be anything, just as long as they're primes.

[Epsilon=One]

I need to find series of 3 prime numbers that are in the form of

P+0(16), P+1(16), P+2(16).

The numbers can be anything, just as long as they're primes.If I understand the problem correctly and you are in base 10, there is no such sequence of prime numbers.

Prime numbers are either Par1 or Par3 numbers. 16 is a Par Number; thus, your series will be 3 consecutive Par1 or 3 consecutive Par3 numbers. Either way, one of the three must be divisible by 3; therefore, one of the three will not be prime.

Or more simply, any series of three numbers equally distant, must have one number divisible by three.

However, with Natural prime numbers (http://www.physicsmathforums.com/showthread.php?t=122) there are many such series of three numbers.

Another interesting prime number question is: Why are there so many pairs of conventional prime numbers (separated by 2) such as: 11, 13; 17,19; 29,31; 41,43; ... 101,103; etc.?

Or, Why is the distribution approximately the same number of primes in any large group of numbers; such as, adjacent groups of 1,000 nunbers or adjacent groups of 5,000 numbers, etc.?