> The precise explanation is complicated, but hinges on the fact that 163 is what is called a Heegner number.
These are the nine Heegner numbers:
1, 2, 3, 7, 11, 19, 43, 67, 163
Here is a python session:
>>> import gmpy2
>>> gmpy2.get_context().precision=1000
>>> pi = 2*gmpy2.acos(0.)
>>> f = lambda i : gmpy2.exp(pi * gmpy2.sqrt(i))
>>> f(163)
mpfr('262537412640768743.99999999999925007259719818568...
> Or take the mathematical relationship fancifully known as “Monstrous Moonshine.”
I wouldn't qualify this as a near miss... This relationship has been shown to hold exactly. I guess in this equation "196,884 = 196,883 + 1", the +1 looks like a glitch, but if you look at the larger pattern it is not a glitch.
These are the nine Heegner numbers: 1, 2, 3, 7, 11, 19, 43, 67, 163
Here is a python session:
> Or take the mathematical relationship fancifully known as “Monstrous Moonshine.”I wouldn't qualify this as a near miss... This relationship has been shown to hold exactly. I guess in this equation "196,884 = 196,883 + 1", the +1 looks like a glitch, but if you look at the larger pattern it is not a glitch.