if we have the following: $[(p_1)(p_2)(p_3)......(p_n)]+1$ where $p_n$ is the nth prime number, and $p_1,p_2...$ are all the prime numbers below $p_n$, is $[(p_1)(p_2)(p_3)......(p_n)]+1$ a prime number?

When i plugged in random numbers into the thing I thought that it was true but then obviously there are prime number generators on computers so it seemed as if $[(p_1)(p_2)(p_3)......(p_n)]+1$ shouldn't always be prime for a number $n$

How do i prove or demonstrate that $[(p_1)(p_2)(p_3)......(p_n)]+1$ isn't always prime?

  • $\begingroup$ What does your notation, $[(p_1)(p_2)] $, mean? $\endgroup$ – infinitylord Jun 2 '17 at 19:54
  • $\begingroup$ I think it is just multiplication, the $[]$ are probably redundant, maybe it seemed clearer to OP $\endgroup$ – Gregory Jun 2 '17 at 19:55
  • $\begingroup$ Counterexample is a perfectly valid method. Try $n=6$. $\endgroup$ – Rocket Man Jun 2 '17 at 19:55
  • 3
    $\begingroup$ $(2)(3)(5)(7)(11)(13) + 1 = 30031$. What are the factors of that? $\endgroup$ – Gregory Jun 2 '17 at 19:57
  • $\begingroup$ I am sure Gregory knew $30031= 59 \times 509$ @infinitylord $\endgroup$ – Donald Splutterwit Jun 2 '17 at 20:18

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