#! perl -slw use strict; use overload; use Math::Big::Factors qw[ factors_wheel ]; use List::Util qw[ reduce min ]; use Algorithm::Loops qw[ NestedLoops ]; my $NUM = $ARGV[ 0 ] || 996; my $root = sqrt $NUM; my @pfs = reverse map{ "$_" } factors_wheel( $NUM ); print "$NUM primefactors ( @pfs )"; my $n = $pfs[ 0 ]; while( @pfs > 1 ) { # print "@pfs"; my $near = reduce{ ( $a * $b ) <= $root ? $a*$b : $a } @pfs; # print "$near : ", $NUM%$near; $n = $near if ( $NUM % $near ) == 0 and abs( $root - $near ) < abs( $root - $n ); my $discard = shift @pfs; next if $pfs[ 0 ] == $discard; unshift @pfs, $pfs[0] while $root > reduce{ $a * $b } @pfs; } print "$NUM ($root} : $n"; __END__ P:\test>432558 1995 1995 primefactors ( 19 7 5 3 ) 1995 (44.6654228682546} : 35 P:\test>432558 1994 1994 primefactors ( 997 2 ) 1994 (44.6542271235322} : 997 P:\test>432558 1993 1993 primefactors ( 1993 ) 1993 (44.6430285710994} : 1e+099 P:\test>432558 1993 1993 primefactors ( 1993 ) 1993 (44.6430285710994} : 1993 P:\test>432558 1994 1994 primefactors ( 997 2 ) 1994 (44.6542271235322} : 997 P:\test>432558 1995 1995 primefactors ( 19 7 5 3 ) 1995 (44.6654228682546} : 35 P:\test>432558 9999999 9999999 primefactors ( 4649 239 3 3 ) 9999999 (3162.27750205449} : 2151 P:\test>432558 99999999 99999999 primefactors ( 137 101 73 11 3 3 ) 99999999 (9999.99995} : 7373 P:\test>432558 999999999 999999999 primefactors ( 333667 37 3 3 3 3 ) 999999999 (31622.7765858724} : 2997 P:\test>432558 1000 1000 primefactors ( 5 5 5 2 2 2 ) 1000 (31.6227766016838} : 25 P:\test>432558 2000 2000 primefactors ( 5 5 5 2 2 2 2 ) 2000 (44.7213595499958} : 40 P:\test>432558 20000 20000 primefactors ( 5 5 5 5 2 2 2 2 2 ) 20000 (141.42135623731} : 125 P:\test>432558 200000 200000 primefactors ( 5 5 5 5 5 2 2 2 2 2 2 ) 200000 (447.213595499958} : 400