Would a summation of floor[cos^2π(((j1)!+1)/j)] from j=1 to x be the same as π(x)?
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$\begingroup$ I cannot read the formula, sorry. The first $\pi$ is the number Pi ? $\endgroup$ – Dietrich Burde Jun 12 '13 at 18:29

$\begingroup$ It's probably off by 1. But why do you ask? $\endgroup$ – Steven Landsburg Jun 12 '13 at 18:34

$\begingroup$ Do you mean I should not ask what the formula is ? Is $\pi ((j1)!+1)$ the prime counting function, or $(j1)!+1$ times $\pi$ ? $\endgroup$ – Dietrich Burde Jun 12 '13 at 18:43

4$\begingroup$ This looks like Wilson's Theorem in disguise. $\endgroup$ – Barry Cipra Jun 12 '13 at 18:43

$\begingroup$ @Dietrich, I think Steven's comment and question was directed to the OP, not to you. $\endgroup$ – Barry Cipra Jun 12 '13 at 18:45