Prime Curios!: 24137

24137
(another Prime Pages' Curiosity)

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The prime that needed the larger R for satisfying de Legendre's formula for the number of primes less than or equal to x;

(x) = x/(ln(x) - r). I.e., 24137 is the 2688th prime and that value is produced by the formula when r = 1.111963. No other prime needs so large an r for producing the true value of

(x) when any x is given. [Dusart]

Submitted: 2009-08-01 19:23:28; Last Modified: 2009-08-01 20:49:58.