cwhmisc (version 6.0)

factor: Create primes, factor an integer, combine factors, check if prime

Description

Create primes, determine the prime factors of an integer together with their multiplicities, recombine factors, primitive version of the sieve of Eratosthenes.

Usage

primes(n)
Eratosthenes(n)
factorN(n)
prodN(fp)
is.prime(n)

Arguments

n

positive integer, number of primes, number to be factored, to be tested

fp

2-colummn matrix with prime factors and multiplicities

Value

primes

Generate the first n primes, also found in PRIMES.

Eratosthenes

Execute the sieve of Eratosthenes.

factorN

Determine the prime factors together with their multiplicities.

prodN

Recombine factors, inverse of factorN.

is.prime

Check if positive integer is prime.

PRIMES

The first primes up to 17389.

Examples

(p <- factorN( 423))
## [1,]   3 47
## [2,]   2  1
# meaning 423 = 3^2 * 47^1
prodN(p) # 423
is.prime(.Machine$integer.max) # TRUE
is.prime(16) # FALSE
## check speed of your machine
  s <- Sys.time(); p<-primes(10^4);difftime(Sys.time(),s) 
## Time difference of 2.906242 secs  on my machine  
x <-factorN(.Machine$integer.max)