Create primes, factor an integer, combine factors, check if prime
Create primes, determine the prime factors of an integer (first row) together with their multiplicities (second row), recombine factors, primitive version of the sieve of Eratosthenes.
primes( n) Eratosthenes( n ) factorN( n ) allFactors( n ) prodN( fp ) is.prime( n )
n |
positive integer, number of primes, number to be factored, to be tested |
fp |
2-colummn matrix with prime factors and multiplicities |
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. |
allFactors |
generate all factors of n: 1..n. |
prodN |
Recombine factors, inverse of factorN. |
is.prime |
Check if positive integer is prime. |
PRIMES |
The first primes up to 17389. |
Christian W. Hoffmann <hristian@echoffmann.ch>
(p <- factorN( 423)) ## [1,] 3 47 ## [2,] 2 1 # meaning 423 = 3^2 * 47^1 prodN(p) # 423 is.prime(.Machine$integer.max) # TRUE is.prime(16) # FALSE ## check speed of your machine s <- Sys.time(); p<-primes(10^4);difftime(Sys.time(),s) ## Time difference of 1.578922 secs on my machine x <- factorN(.Machine$integer.max)
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