`factor`

: Print prime factors`factor`

prints prime factors. Synopsis:

factor [option]… [number]…

If no `number` is specified on the command line, `factor`

reads
numbers from standard input, delimited by newlines, tabs, or spaces.

The program accepts the following options. Also see Common options.

- ‘
`-h`’ ¶ - ‘
`--exponents`’ -
print factors in the form

*p^e*, rather than repeating the prime ‘`p`’, ‘`e`’ times. If the exponent ‘`e`’ is 1, then it is omitted.$ factor --exponents 3000 3000: 2^3 3 5^3

If the number to be factored is small (less than *2^{127}* on
typical machines), `factor`

uses a faster algorithm.
For example, on a circa-2017 Intel Xeon Silver 4116, factoring the
product of the eighth and ninth Mersenne primes (approximately
*2^{92}*) takes about 4 ms of CPU time:

$ M8=$(echo 2^31-1 | bc) $ M9=$(echo 2^61-1 | bc) $ n=$(echo "$M8 * $M9" | bc) $ bash -c "time factor $n" 4951760154835678088235319297: 2147483647 2305843009213693951 real 0m0.004s user 0m0.004s sys 0m0.000s

For larger numbers, `factor`

uses a slower algorithm. On the
same platform, factoring the eighth Fermat number *2^{256} + 1*
takes about 14 seconds, and the slower algorithm would have taken
about 750 ms to factor *2^{127} - 3* instead of the 50 ms needed by
the faster algorithm.

Factoring large numbers is, in general, hard. The Pollard-Brent rho
algorithm used by `factor`

is particularly effective for
numbers with relatively small factors. If you wish to factor large
numbers which do not have small factors (for example, numbers which
are the product of two large primes), other methods are far better.

An exit status of zero indicates success, and a nonzero value indicates failure.