42 is not a particularly significant number mathematically.

However some numbers are very special, especially those that are integers and 42 just missed two them. 41, from

Euler's prime generating polynomial, and 43, which is one of the eight

Heegner numbers 1, 2, 3, 7, 11, 19, 43, 67, 163. The

Fibonacci Numbers are better known but they are an infinite sequence. The Heegner Numbers are a small finite set which make them very special.

The first couple of Heegner Numbers are considered trivial. The last three participate in an interesting expression that includes three irrational expressions but whose results are incredibly

close to being integers, especially with 163.

The ratio of the diameter of a circle to its radius (Pi) is an irrational number (no patterns in the sequence of digits), as are most square roots. The Natural Number (e) is the irrational number where the log to the base of the Natural Number is itself.

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Yet the Natural Number raised to the square root of the product of any of these three numbers and pi is almost an integer, in the case of 163, to twelve decimal places.

The reasons for this are not mathematical accidents. They are fundamentally related to the

Golden Ratio. This unique irrational number is x where