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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 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 about 80 seconds of CPU time on a 1.6 GHz Athlon.

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

Similarly, it takes about 80 seconds for GNU factor (from coreutils-5.1.2) to “factor” the largest 64-bit prime:

 
$ factor 18446744073709551557
  18446744073709551557: 18446744073709551557

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

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


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