One more big scary math formula, for those who may be interested.
Brun's Constants measure the frequency of Prime numbers, and have proven pertinent in breaking encryption algorithms. In particular, Brun's Quadratic Constant measures the rate at which four primes occur in a row. A prime number is one which is divisible only by itself and 1, and a twin prime number is a pair of prime numbers separated by no more than two, while a prime quadruplet is a pair of twin primes back to back. The first such quadruplet is (5, 7, 11, 13). Divide each of those numbers by one, and add the result, then repeat that step for all other twin prime quadruplets, and the resulting infinite sum asymptotically approaches Brun's Quadratic Constant.
One of the equations I shared found remarkable correlation between the Quadratic Constant and both the Twin Prime and Khinchin Constants, as well as with Pi. As with the other pseudo-equations, I have no real explanation for why this is the case. It could be accurate, but Brun's Quadratic Constant is as yet only known to a few decimal digits, so there's no way to verify.
Brun's Quadratic ~= acosh((10^2)^((Twin Prime)/((Khinchin) + 2 * Pi)))
{Twin Prime = 0.66016181584686957; Khinchin = 2.68545200111950741674; Pi = 3.14159265358979323846264}
B4 ~= cosh-1((102)C2/(K0 + 2*π))
{C2 = Twin Prime; K0 = Khinchin; π = Pi}
B4 ~= 0.87058837975732789829539157590687201690364844571784554175631344760322630394
I would also like to share some conjecture:
You may have noticed that most of these equations are off by a tiny amount. You may also have noticed that a lot of them involve the number 10. That came as a complete surprise to me, as 10 is not supposed to have any real significance, other than as a basis for humanity's number system. Otherwise, it is just one out of an infinite array of integers. So why would universal mathematical constants depend upon it?
My hypothetical answer is that the number 10 which keeps appearing may itself be the result of a calculation based on yet more mathematical constants, all of which may or may not have been discovered yet. Setting the 10 to a variable (e.g. ζ) and then solving for it yields a number slightly greater than ten, and that number itself has remained remarkably consistent across each of these equations.
I have as yet no means to reliably figure out what mathematical constants (if any) must be combined together to approach ζ, and would call upon those with greater mathematical skill than I to figure that out.
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