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Keywords: PrimeNumberTheorem.png Displayed is the number of primes less than or equal to x labelled <math>\Pi x </math> red an approximation using <math>\frac x \ln x </math> green an approximation using the logarithmic integral <math>\operatorname Li x </math> blue Created with Maple plot seq x pi x x 0 100000 x/ln x Li x -Li 2 x 0 100000 Pix 0 10000 color blue green red ; Author FredStober PrimeNumberTheorem svg FredStober Prime numbers Functions Scatterplots of integer sequences |