Abstract:
The perfect cuboid problem is a Pythagorean problem in nature. This
paper gives several propositions regarding Pythagorean relationships and
a discussion is made on the perfect cuboid problem. Among the proposi-
tions is that the cuboid problem is a divisibility by 3 problem. Violation
of the divisibility means that a perfect cuboid doesn’t exist for a given
integer.
Another consequence of divisibility by 3 and other theorems is that
the fastest and most accurate algorithm for generating a random prime
number p is,
p =
(5 × β) 2 + 1
2
where β = 2k + 1, k ∈ N.
