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Re^2: Math help: Finding Prime Numbers

by I0 (Priest)
on Nov 25, 2006 at 08:25 UTC ( #585990=note: print w/ replies, xml ) Need Help??


in reply to Re: Math help: Finding Prime Numbers
in thread Math help: Finding Prime Numbers

my $Limit = 1000000; my $HighestFactor = sqrt($Limit); my $is_prime=''; # Sieve array. # put in candidate primes: integers which have an odd number of repres +entations by certain quadratic forms. for $x ( 1..$HighestFactor){ my $x2 = $x*$x; last if $x2*2 >= $Limit; for $y ( 1..$HighestFactor ){ my $y2 = $y*$y; next if ($n = 3*$x2 - $y2) > $Limit; vec($is_prime,$n,1) ^= 1 if $x > $y && $n % 12 == 11; next if ( $n = 3*$x2 + $y2 ) > $Limit; vec($is_prime,$n,1) ^= 1 if $n % 12 == 7; next if ( $n = 4*$x2 + $y2 ) > $Limit; vec($is_prime,$n,1) ^= 1 if $n % 12 == 1 || $n % 12 == 5; } } # eliminate composites by sieving # if n is prime, omit all multiples of its square; this is sufficient +because # composites which managed to get on the list cannot be square-free for $n (5..$HighestFactor ){ next unless vec($is_prime,$n,1); for( $k=$n2=$n*$n; $k <= $Limit; $k += $n2 ){ vec($is_prime,$k,1) += 0 }; } # Present the results. $\="\n"; print for 2,3, grep vec($is_prime,$_,1), 5..$Limit;


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