for Bernard proveth that if p > 7 then
p^6 = 1 + 84n
and thus 84 is the full proven truth, twice the truth of 42. However 84 is but an imposter of the full proven truth. As Bernard showeth, for p an odd prime, p^3 is an odd number, and consequently both (p^3 - 1) and (p^3 + 1) are even, but as they are consecutive even numbers then one must be divisible by 4, hence:
(p^6 - 1) = (p^3 - 1) * (p^3 + 1) = 2*a * 4*b = 8*a*b
Thus we have the next full proven truth that
p^6 = 1 + 168n
But there is more... As p is prime, then the residue modulo 9 shall be one of {+/- 1, +/- 2, +/- 4} which using the fact that 2^3 = 8 = -1(mod 9), and 4 = 2^2 so 4^3 = 2^6 = 1(mod 9), then p^3 = +/- 1 (mod 9), then p^6 = 1 (mod 9) and hence:
(p^6 - 1) = 9*c
And so we have the next proven truth that if p is prime and p is not 2,3 or 7 then:
p^6 = 1 + 504n
and the full truth is that there is no number higher than 504 to satisfy this.
Peter "Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."