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 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.

In the number 6210001000:

• The digit 0 occurs 6 times
• The digit 1 occurs 2 times
• The digit 2 occurs 1 time
• The digit 3 occurs 0 times
• The digit 4 occurs 0 times
• The digit 5 occurs 0 times
• The digit 6 occurs 1 time
• The digit 7 occurs 0 times
• The digit 8 occurs 0 times
• The digit 9 occurs 0 times

See also The Quick Brown Fox …

115132219018763992565095597973971522401 = 1³⁹ + 1³⁹ + 5³⁹ + 1³⁹ + 3³⁹ + 2³⁹ + 2³⁹ + 1³⁹ + 9³⁹ + 0³⁹ + 1³⁹ + 8³⁹ + 7³⁹ + 6³⁹ + 3³⁹ + 9³⁹ + 9³⁹ + 2³⁹ + 5³⁹ + 6³⁹ + 5³⁹ + 0³⁹ + 9³⁹ + 5³⁹ + 5³⁹ + 9³⁹ + 7³⁹ + 9³⁹ + 7³⁹ + 3³⁹ + 9³⁹ + 7³⁹ + 1³⁹ + 5³⁹ + 2³⁹ + 2³⁹ + 4³⁹ + 0³⁹ + 1³⁹