25.1 factor: Print prime factors

factor prints prime factors. Synopses:

factor [number]... factor option

If no number is specified on the command line, factor reads numbers from standard input, delimited by newlines, tabs, or spaces.

The only options are `--help' and `--version'. See section 2. Common options.

The algorithm it uses is not very sophisticated, so for some inputs factor runs for a long time. The hardest numbers to factor are the products of large primes. Factoring the product of the two largest 32-bit prime numbers takes over 10 minutes of CPU time on a 400MHz Pentium II.

$ p=`echo '4294967279 * 4294967291'|bc` $ factor $p 18446743979220271189: 4294967279 4294967291

In contrast, factor factors the largest 64-bit number in just over a tenth of a second:

$ factor `echo '2^64-1'|bc` 18446744073709551615: 3 5 17 257 641 65537 6700417