Thirteen characters · 251,643 digits

The
number

43 × 2⁸³⁵⁹³⁴ + 1

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Thirteen characters that expand into 251,643 digits — a compression of roughly nineteen thousand to one. The recipe is thirteen characters long. The dish runs a hundred and fifty pages.

43 × 2⁸³⁵⁹³⁴ + 1, streaming. Read aloud at two digits a second, the whole number takes about thirty-five hours.

Digits

251,643

Found by

Curtis Cooper, University of Central Missouri, 11 July 2006

Catalogued

Entry 78105 in the PrimePages database

Proven

By Proth's theorem — not probably prime, provably prime

Read aloud

About 35 hours at two digits a second

Every digit has to be exactly what it is

Change any single one of the 251,643 and the number almost certainly stops being prime. There are no typos in the book, because a typo would make it a different book.

Check it yourself

You do not have to take anyone's word for this, which is the entire point of a proof. On an ordinary laptop it takes less time than reading this page.

python3 -c "
from sympy import isprime
print(isprime(43 * 2**835934 + 1))
"

The people who found and proved this number never had a reason to look at its digits. It was known the way a mountain can be mapped without being climbed — through formulas, tests and proofs.

And it was prime before the Earth existed

Every date in the book is a date on which humans learned something. Nothing has ever happened to the number itself.