How to derrive prime density function pi(x)=x/ln(x) ??
2007-05-11 08:28:32 · 4 answers · asked by arunjayendran0707 2 in Science & Mathematics ➔ Mathematics
This result, pi(x) asymtotic to x/lnx, was first proven in 1896
by both de la Vallee Poussin and Hadamard. A result by Rosser&Schoenfeld (1962), gives pi(x)>= x/lnx if x >=11.
Then Dusart (1998) proved that pi(x)
and pi(x)>x/(lnx-1) if x>5393.
2007-05-11 09:58:21 · answer #1 · answered by knashha 5 · 0⤊ 0⤋
I think that was found imperically. But if you do discover that derivation, the corporate world would be extremely interested, since prime numbers have great importance in security and cryptology.
2007-05-11 08:46:43 · answer #2 · answered by jsardi56 7 · 0⤊ 0⤋
Yes
2016-05-20 23:01:52 · answer #3 · answered by chrystal 3 · 0⤊ 0⤋
That is only true asymptotically, so what you have written is not an equality, but an asymptotic (like lim(x-->inf)).
I don't remember the exact derivation; my algebra class was some time ago.
2007-05-11 09:34:54 · answer #4 · answered by acafrao341 5 · 0⤊ 0⤋