My professor showed the class 1000 dollars and said he'd give it to whoever could prove it... Obviously he's not serious but in having a tough time wrestling with this problem.
2026-03-26 11:00:47.1774522847
Are there infinitely many semi primes of the form $x^2 + 2x$ for integral $x$?
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It is likely that no one in the class will collect. Since $x^2+2x=x(x+2)$, for $x\gt 2$ we have $x^2+2x$ is semiprime if and only if $x$ and $x+2$ are twin primes. Whether there are infinitely many twin primes is a longstanding open problem.
Remark: From a professional point of view, the interesting part is that the professor has $\$1000$ to show. Perhaps an inheritance.