# Eddington number

"I believe there are 15, 747, 724, 136, 275 ,002, 577, 605, 653,
961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185,
631, 031, 296 protons in the universe and the same number of electrons."
So wrote the English astrophysicist Sir Arthur Eddington in his book *Mathematical Theory of Relativity* (1923). Eddington arrived
at this outrageous conclusion after a series of convoluted (and wrong!)
calculations in which he first "proved" that the value of the so-called fine-structure constant was exactly 1/136. This value appears as a factor in his prescription for
the number of particles (protons + electrons; neutrons were not discovered until 1930)
in the universe: 2 × 136 × 2^{256} = 17 × 2^{260} = 3.149544...
× 10^{79} (double the number written out in full in the quote above).
This is the Eddington number, notable for being the largest *specific* integer (as opposed to an estimate or approximation) ever thought to have
a unique and tangible relationship to the physical world. Unfortunately,
experimental data gave a slightly lower value for the fine-structure constant,
closer to 1/137. Unfazed, Eddington simply amended his "proof" to show that
the value had to be exactly 1/137, prompting the satirical magazine *Punch* to dub him "Sir Arthur Adding-One."