Hate exponents? Just cancel them:

See also Reductio Ad Absurdum.

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:

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 http://7427466391.com 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.

Type 120121 into a calculator and you’ll find it’s prime every way you look at it: right side up, upside down (121021), in a mirror (151051), or both (150151).

35 – 3² – 5² = 75 – 7² – 5²

144648 = 861 × 168 = 492 × 294

185472 = 672 × 276 = 384 × 483

9949716 = 2583 × 3852 = 1476 × 6741

16746912 = 2556 × 6552 = 4473 × 3744

Every even number greater than 2 (black) is the sum of two primes.

Is that true? No one knows. Originally proposed in 1742, it’s been tested as far as 10¹⁸, but the jury’s still out.