http://www.engert.us/erwin/miscellaneous/William%20Shanks%20707%20digits.pdf I believe the "707 digits" refers to decimal places. The first 527 (excluding typos) were correct. I think your difference is 696972233400402414486921529175050301808106570457226115312565026347185368614269829439388229424273703513612402766518096376765306056957758635728165741884423700490282252529162636899/10^706. On Jul 14, 2014, at 10:27 AM, James Propp <jamespropp@gmail.com> wrote:

Does anyone know what precise error (or errors) William Shanks made?

E.g., if you take the difference between Shanks' 707-digit approximation to pi and the 707-digit truncation of pi, do you get the initial digits of some rational number?