# The Digits of Pi and e

Im a math learner so the questions may seem obvious.

With it being pi day the 14th of this month the digits of pi have been in my thoughts. The BBP algorithm for Pi enables the computation of any binary digit of pi wthout computing all the previous digits. The BBP algorithm can be implemented without special data structures & just using the non-custom data types already built in to a programming language such as C++ or Ruby. The complexity of the algorithm is polynomial space and quasi-linear time. So for example the 40 digit of Pi can be computed without computing the previous 39 digits of Pi using the BBP algorithm. My question is is there such a BBP algorithm for e (approx 2.71828)?-I could not find such an algorithm and wondered if there is a provable reason why it should not exist. So the algorithm for e would not require to compute all the previous digits-up to the require digit-and not have a worser complexity than the BBP algorithm for Pi. The BBP algorithm I refer to is based on the series given at the top of

https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

If such an algorithm does not exist then how do you use PSLQ algorithm, if possible, to find it?

• I have had no luck finding a digit extraction algorithm for e, but this is indeed the technical term that you are looking for. – Ian Mar 30 '16 at 1:59