Euler’s Identity

You know these numbers:


On the surface they appear unrelated. e is the base of natural logarithms, i is imaginary, π concerns circles. But, amazingly:

Euler's identity

Harvard mathematician Benjamin Peirce told a class, “It is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.”


In 2004 a mysterious billboard appeared in Silicon Valley; Cambridge, Mass.; Seattle; and Austin, Texas. It read:

{first 10-digit prime found in consecutive digits of e}.com

Most people know that e (2.718281828 …) is the base of natural logarithms, but searching it for a 10-digit prime string is a considerable task — the first such string, 7427466391, starts at the 101st digit.

Solvers who went to found an even more difficult problem to solve. But solving that led them to a page at Google Labs … inviting them to submit a resume.