cwhmisc (version 5.0)

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$integer.max) # TRUE
## check speed of your machine
  s <- Sys.time(); p<-primes(10^4);difftime(Sys.time(),s) 
## Time difference of 8.36586 secs  on my machine  
x <-factorN(.Machine$integer.max)