If you want more precision, you might be interested in Unbounded Spigot Algorithms for the Digits of π by Jeremy Gibbons. It's a fun read, and you can adapt the methods presented in his paper to computing e digit by digit.
In reply to Good to about 45 places; spigot algorithm
by tmoertel
in thread e with continued fractions
by jdalbec
| For: | Use: | ||
| & | & | ||
| < | < | ||
| > | > | ||
| [ | [ | ||
| ] | ] |