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pracma (version 1.9.3)

primes: Prime Numbers

Description

Generate a list of prime numbers less or equal n, resp. between n1 and n2.

Usage

primes(n)

Arguments

n
nonnegative integer greater than 1.

Value

vector of integers representing prime numbers

Details

The list of prime numbers up to n is generated using the "sieve of Erasthostenes". This approach is reasonably fast, but may require a lot of main memory when n is large.

In double precision arithmetic integers are represented exactly only up to 2^53 - 1, therefore this is the maximal allowed value.

See Also

isprime, factors

Examples

Run this code
primes(1000)
## Not run: 
# ##  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
# # --------------------------------------## End(Not run)

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