Hi,
I have a conjecture, it might be common sense, but I think it is interesting and would appreciate and feedback.
One result of this overall graph is that given a prime p, for all numbers n > p where n-p is a prime number, there is a decreasing likelihood that n+p will be a prime number based on how many multiples of 2,6,30,210,2310 and higher primorials n is a multiple of. Ie for n that are only multiples of 2, it is least common that n+p is prime. Also when n is a multiple of 2,6,30,210,2310 and higher primorials, it is most common that n+p will be a prime number.
The definitions I used:
z(x y) Prime pair of n definition: For a given number n and for two primes x and y, with x between 0, and y between n and 2n, if n-x is equal to y-n, then x and y are called a prime pair z(x y) of n.
Z(x y) Primal pair: For prime pair z(x y) if n-x is a prime number then prime pair z is called a primal pair Z(x y). It follows if n-x is a prime number then y-n is also a prime number as y-n = n-x
The partially completed graph built from the above definitions (doesn't show peaks of primorial 2 yet)
Y-axis is Z(x y) count for each x-axis n:
cheers, Jamie