Exactly what the name entails. The function $2^n-1$ I see largely tends to generate primes when $n$ is prime. However, a week ago I heard that this was horribly false. Please show me a disproof.

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    $\begingroup$ Often when you want to prove something like this isn't true, you just search for examples. $\endgroup$ – Cameron Williams Jul 5 '15 at 5:16
  • $\begingroup$ you only need one case to disprove something, like a truth table in this case going to infinity. $\endgroup$ – miniparser Jul 5 '15 at 5:38
  • $\begingroup$ Even though experimental evidence strongly suggests that for most primes, $2^p-1$ is not prime, it has not been shown that there are infinitely many primes $p$ such that $2^p-1$ is not prime. $\endgroup$ – André Nicolas Jul 5 '15 at 5:45

$$\Large 2^{11}-1=23\cdot 89$$ Take a look at the Wikipedia page on Mersenne primes. There are (currently) only $48$ known prime numbers $p$ such that $2^p-1$ is prime, after people have used computers to check millions.

  • $\begingroup$ Well that answers it $\endgroup$ – AAron Jul 5 '15 at 5:10

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