Python: Computing \$e\$ [closed]

Question

I was trying to solve a problem which stated:

Calculate the first 10 digit prime found in consecutive digits of e.

I was able to solve the problem but I did it by using some 10k digits of e available online. So I tried to write a program which calculates digits of e. The problem is that it simply gives the incorrect answer.

The code and the formula I used are:

$$e = \sum\limits_{n=0}^{\infty}\frac{1}{n!} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1 \cdot 2} + \frac{1}{1\cdot 2 \cdot 3} + \cdots$$

import math

e=0

x=int(input()) #larger this number, more will be the digits of e

for i in range(x):
    e+=(1/(math.factorial(i)))

print(e)

When the user inputs 10, the digits returned are 2.7182815255731922 which is not correct.

Can someone explain why my code does not produce the correct result?

Answer 1

First of all, don't panic. 10 is just not enough (indeed, it only gives you 5 decimal places. Try 20, and obtain

2.71828182846

which is much closer.

Now, Python uses a native floating point, which may only give you that many digits of precision (say, 30). To get more, you need to work with another representations; fractions.Fraction looks like a good candidate.

Finally, calls to math.factorial waste too much computing power. It is better to compute factorials as you go, e.g.

    denom = 1
    for i in range(1, x):
        e += 1 / denom
        denom *= i