OFFSET
2,1
COMMENTS
prime(n) ~ n*log(n)+n-n*log(log(n)) - (n/log(n))*(log(log(n))-2)+(log(log(n))-6)*n*log(log(n))/(2*log(n)^2))
REFERENCES
M. Cipolla, "La determinazione asintotica dell'n-mo numero primo.", Rend. d. R. Acc. di sc. fis. e mat. di Napoli, s. 3, VIII (1902), pp. 132-166.
LINKS
Pierre Dusart, Estimates of Some Functions Over Primes without R.H. (2010).
Wikipedia, Prime number theorem
MATHEMATICA
Table[Floor[Prime[n]-n*Log[n]+n-n*Log[Log[n]]- (n/Log[n]) (Log[Log[n]]-2)+(Log[Log[n]]-6)*n*Log[Log[n]]/(2*Log[n]^2)], {n, 2, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
José María Grau Ribas, Jan 14 2012
STATUS
approved