Mark sieve [ n ] is true if one of the following is true : a ) n = ( 4 * x * x ) + ( y * y ) has odd number of solutions , i . e . , there exist odd number of distinct pairs ( x , y ) that satisfy the equation and n % 12 = 1 or n % 12 = 5. b ) n = ( 3 * x * x ) + ( y * y ) has odd number of solutions and n % 12 = 7 c ) n = ( 3 * x * x ) - ( y * y ) has odd number of solutions , x > y and n % 12 = 11
for ( $ x = 1 ; $ x * $ x < $ limit ; $ x ++ ) { for ( $ y = 1 ; $ y * $ y < $ limit ; $ y ++ ) {