163

In the April 1975 issue of Scientific American, Martin Gardner reported as fact that e raised to π√163 had been shown to be exactly an integer, attributing the discovery to Ramanujan. It was an April Fools' item — the expression differs from a whole number in the twelfth decimal place — and the joke worked precisely because the near-miss is real and startling. The name 'Ramanujan's constant' for the quantity dates from the hoax rather than from Ramanujan, who never claimed it.

There are exactly nine Heegner numbers — 1, 2, 3, 7, 11, 19, 43, 67 and 163 — and 163 is the largest. Kurt Heegner, a radio engineer working outside the university system, published a proof of the completeness of the list in 1952; it was dismissed as flawed and largely ignored, and only after Stark and Baker independently settled the problem in the late 1960s was Heegner's argument re-examined and found essentially correct. He had died in 1965.

e to the power of pi root 163 differs from a whole number by less than a trillionth. The near-miss follows from 163 being the largest Heegner number, a fact about class numbers proved in the 1950s — so the coincidence has an explanation rather than being one.