Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any result, that says that $\lfloor e^{n} \rfloor$ is never a prime for $n > 2$ ?

share|cite|improve this question
$\lfloor e^{18} \rfloor = 65659969$ is a prime. – achille hui Sep 19 '13 at 10:45
@achillehui Can I ask how you checked that? Did you just quickly write some code, check a website, or is there a remarkable insight hidden in your answer? – snarski Sep 19 '13 at 12:56
@smarski I just use a computer algebra system (maxima in my case) to compute the first few terms. Whenever one see a claim like this, the first thing one should do is check the obvious cases before one investing time to prove it. – achille hui Sep 19 '13 at 13:14
@achillehui And the obvious cases are the first several dozen? – sasha Sep 19 '13 at 20:33
@sasha, Whatever that doesn't take too long to type and too long to run. In this case, the first several dozen. – achille hui Sep 20 '13 at 2:32

The counterexamples up to 1000 are:

18, 50, 127, 141, 267, 310
share|cite|improve this answer
See also – lhf Sep 19 '13 at 12:32

There is no such result, because $\lfloor e^{18} \rfloor = 65659969$ is prime. This is the smallest counterexample.

share|cite|improve this answer

Nope for $n=18$ we have

$$\lfloor \exp(18)\rfloor =65659969$$ which is prime

The counterexamples for $n\leq 10000$ you have \begin{array}{c} 18\\ 50\\ 127\\ 141\\ 267\\ 310\\ 2290\\ 4487\\ 5391\\ \end{array}

share|cite|improve this answer
See also – lhf Sep 19 '13 at 13:01
Typo of 8 instead of 18 in your list I believe. – Chris Sep 19 '13 at 16:11
@Chris in fact I wrote 18 but forgot to center the array so he took the 1 as the positioning letter (r,l,c) – Dominic Michaelis Sep 19 '13 at 20:26

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.