Solve This

A long time ago Goldbach formulated his famous claim that every even number greater than or equal to two can be represented as the sum of two primes. For example, 8 = 5 + 3. At the beginning of the last century Hilbert, while compiling his list of the great unproven conjectures of mathematics, included Goldbach as well. The claim remains unproven to this day. The most interesting part is that it is completely useless in practical terms — which makes it all the more interesting to mathematicians.

Hilbert's list has grown rather thin and outdated over a whole century. Well then, it's time to add a new problem to it (mine!), one that is an order of magnitude harder and an order of magnitude more useless. Here it is:

Let $\pi(n)$ and $e(n)$ be functions that return the n-th digits of the irrational numbers π and e, respectively. Prove or disprove that for n = 0..∞:

$$\pi(n) = \lim_{N\to\infty} e(N - n),$$

where N is the number of digits in the numbers (N → ∞).

In other words, you need to find out whether π equals e written backwards, with the decimal point put in the right place. There you go.

[update] The problem was solved simply and elegantly by connected — details in the comments. Hooray!