prime-counting function | Desmos

Expression 1: pi Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals Start sum from "k" equals 1 to "x" , end sum, left parenthesis, 1 minus floor left parenthesis, round left parenthesis, left parenthesis, StartFraction, sin left parenthesis, StartNestedFraction, pi NestedOver 2 , EndNestedFraction floor left parenthesis, "k" , right parenthesis , right parenthesis Over StartNestedFraction, pi NestedOver 2 , EndNestedFraction floor left parenthesis, "k" , right parenthesis , EndFraction , right parenthesis , right parenthesis plus left parenthesis, left parenthesis, Start product from "n" equals 2 to floor left parenthesis, "k" , right parenthesis minus 1, end product, left parenthesis, mod left parenthesis, floor left parenthesis, "k" , right parenthesis , "n" , right parenthesis , right parenthesis , right parenthesis plus 1 , right parenthesis to the negative 1st power , right parenthesis , right parenthesis Has graph. To audio trace, press ALT+T.

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