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If $p$ and $q$ are prime numbers, then $pq+1$ is prime. I don't really know how this can be proven, I've used prime numbers to plug in but I don't know how the steps should go.

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    Odd times odd is ... – 2017-01-30
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    Even 3 times 3 =6 – 2017-01-30
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    That's a good one! But seriously... – 2017-01-30
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    This is almost always false, because if $p$ and $q$ are odd, then $pq+1$ is even – 2017-01-30
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    So how this can be proven tho Ik its – 2017-01-30
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    How can a false statement be proven? Are you kidding? – 2017-01-30
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    The most common case (both primes odd) is known. If $p$ is even and $q$ is odd, *nothing* can be concluded, for example, i) $(p,q) = (2,3)$ so $pq + 1 = 7$ is prime ii) $(p,q) = (2,7)$ so $pq = 15$. The last case $p = q = 2$ is trivial. – 2017-01-30
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    False. For example, $3*5+ 1 = 16$ – 2017-02-23

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The assertion is false, as a (counter) example: $p = 5, q = 7$ are both primes, yet $pq +1 = 5\cdot 7 +1 = 36$ is a composite ! and in general, $pq+1$ is even and $ > 2$, thus can never be a prime.

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    So how this can be proven tho? Ik it's false – 2017-01-30
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    The proof that it's false is that @Deepsea gave a counterexample. – 2017-01-30
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    Ya I know got it – 2017-01-30
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Let $p=13$ and $q=17$. So you have $$pq+1\equiv_3 1*2+1\equiv_3 0$$, so it's divisible by $3$, and clearly it's greater than $3$, so $pq+1$ is composite.

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Numbers $3$ and $7$ are primes, but $3\cdot7+1 = 22 = 2\cdot 11$ is not, hence the proposition is false.