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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)

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

a (typically positive integer) number.

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

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

max(n)

n

Factorize, GCD, LCM, IsPrime

Factorize

GCD

LCM

IsPrime

(p1 <- Primes(100)) system.time(p1k <- Primes(1000)) # still lightning .. stopifnot(length(p1k) == 168)

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