numbers (version 0.6-6)

# primeFactors: Prime Factors

## Description

`primeFactors` computes a vector containing the prime factors of `n`. `radical` returns the product of those unique prime factors.

## Usage

```primeFactors(n)

## Arguments

n

nonnegative integer

## Value

Vector containing the prime factors of `n`, resp. the product of unique prime factors.

## Details

Computes the prime factors of `n` in ascending order, each one as often as its multiplicity requires, such that `n == prod(primeFactors(n))`.

## radical() is used in the abc-conjecture:

# abc-triple: 1 <= a < b, a, b coprime, c = a + b

# for every e > 0 there are only finitely many abc-triples with

`divisors`, `gmp::factorize`

## Examples

Run this code
``````# NOT RUN {
primeFactors(1002001)         # 7  7  11  11  13  13
primeFactors(65537)           # is prime
# Euler's calculation
primeFactors(2^32 + 1)        # 641  6700417

# }
# NOT RUN {
for (i in 1:99) {
for (j in (i+1):100) {
if (coprime(i, j)) {
k = i + j