https://github.com/cran/pracma
Revision 26e049d70b4a1c237987e260cba68f6a9413736c authored by Hans W. Borchers on 09 April 2019, 04:10:07 UTC, committed by cran-robot on 09 April 2019, 04:10:07 UTC
1 parent bf07673
Tip revision: 26e049d70b4a1c237987e260cba68f6a9413736c authored by Hans W. Borchers on 09 April 2019, 04:10:07 UTC
version 2.2.5
version 2.2.5
Tip revision: 26e049d
primes.Rd
\name{primes}
\alias{primes}
\title{Prime Numbers}
\description{
Generate a list of prime numbers less or equal \code{n}, resp. between
\code{n1} and \code{n2}.
}
\usage{
primes(n)
}
\arguments{
\item{n}{nonnegative integer greater than 1.}
}
\details{
The list of prime numbers up to \code{n} is generated using the "sieve of
Erasthostenes". This approach is reasonably fast, but may require a lot of
main memory when \code{n} is large.
In double precision arithmetic integers are represented exactly only up to
2^53 - 1, therefore this is the maximal allowed value.
}
\value{
vector of integers representing prime numbers
}
\seealso{
\code{\link{isprime}, \link{factors}}
}
\examples{
primes(1000)
\dontrun{
## Appendix: Logarithmic Integrals and Prime Numbers (C.F.Gauss, 1846)
library('gsl')
# 'European' form of the logarithmic integral
Li <- function(x) expint_Ei(log(x)) - expint_Ei(log(2))
# No. of primes and logarithmic integral for 10^i, i=1..12
i <- 1:12; N <- 10^i
# piN <- numeric(12)
# for (i in 1:12) piN[i] <- length(primes(10^i))
piN <- c(4, 25, 168, 1229, 9592, 78498, 664579,
5761455, 50847534, 455052511, 4118054813, 37607912018)
cbind(i, piN, round(Li(N)), round((Li(N)-piN)/piN, 6))
# i pi(10^i) Li(10^i) rel.err
# --------------------------------------
# 1 4 5 0.280109
# 2 25 29 0.163239
# 3 168 177 0.050979
# 4 1229 1245 0.013094
# 5 9592 9629 0.003833
# 6 78498 78627 0.001637
# 7 664579 664917 0.000509
# 8 5761455 5762208 0.000131
# 9 50847534 50849234 0.000033
# 10 455052511 455055614 0.000007
# 11 4118054813 4118066400 0.000003
# 12 37607912018 37607950280 0.000001
# --------------------------------------}
}
\keyword{ arith }
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