Find All Primes Less Than n

Find all prime numbers aka ‘primes’ less than \(n\).

Uses an obvious sieve method and some care, working with logical and integers to be quite fast.

Primes(n)

Arguments

n

a (typically positive integer) number.

Details

As the function only uses max(n), n can also be a vector of numbers.

Value

numeric vector of all prime numbers \(\le n\).

Note

This function was previously published in the package sfsmisc as primes and has been integrated here without logical changes.

Author

Bill Venables (\(\le n\)); Martin Maechler gained another 40% speed, working with logicals and integers.

See also

Factorize, GCD, LCM, IsPrime

Examples

(p1 <- Primes(100))
#>  [1]  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
system.time(p1k <- Primes(1000)) # still lightning ..
#>    user  system elapsed 
#>   0.001   0.000   0.001 

stopifnot(length(p1k) == 168)