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1.1       root        1: .TH FACTOR 1 
                      2: .CT 1 numbers
                      3: .SH NAME
                      4: factor, qfactor, primes \(mi factor a number, generate large primes
                      5: .SH SYNOPSIS
                      6: .B factor
                      7: [
                      8: .I number
                      9: ]
                     10: .PP
                     11: .B qfactor
                     12: .PP
                     13: .B primes
                     14: [
                     15: .I start
                     16: [
                     17: .I finish
                     18: ]
                     19: ]
                     20: .SH DESCRIPTION
                     21: .I Factor
                     22: prints
                     23: .I number
                     24: and its prime factors,
                     25: each repeated the proper number of times.
                     26: The number must be positive and less than
                     27: .if n 2**56
                     28: .if t 2\u\s756\s0\d
                     29: (about
                     30: .if n 7.2e16)
                     31: .if t 7.2\(mu10\u\s716\s0\d\|).
                     32: .PP
                     33: If no
                     34: .I number 
                     35: is given,
                     36: .I factor
                     37: reads a stream of numbers from the standard input and factors them.
                     38: It exits on any input not a positive integer.
                     39: Maximum running time is proportional to
                     40: .if n sqrt(n).
                     41: .if t .I \(sr\o'n\(rn'.
                     42: .PP
                     43: .ig
                     44: .I Lfactor
                     45: reads one number from the standard input and factors it.
                     46: Worst-case running time is proportional to
                     47: .if n .IR n **(1/5);
                     48: .if t .IR n \u\s-21/5\s0\d;
                     49: it beats
                     50: .I factor
                     51: for hard 12-digit problems and is workable to around
                     52: .if n .IR n =10**30.
                     53: .if t .IR n =10\u\s-230\s0\d.
                     54: ..
                     55: .I Qfactor
                     56: reads one number from the standard input and factors it.
                     57: It will factor numbers
                     58: up to about 40 digits.
                     59: For large numbers it is much faster than
                     60: .I factor.
                     61: .PP
                     62: .I Primes
                     63: prints the prime numbers ranging from
                     64: .I start
                     65: to
                     66: .I finish,
                     67: where
                     68: .I start
                     69: and
                     70: .I finish
                     71: are positive numbers less than 
                     72: .if n 2**56.
                     73: .if t 2\u\s756\s0\d.
                     74: If 
                     75: .I finish
                     76: is missing,
                     77: .I primes
                     78: prints without end;
                     79: if
                     80: .I start
                     81: is missing, it reads the starting number from the
                     82: standard input.

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