SPOJ prime generator in PHP - php

Question

I am getting time limit exceeded error while I submitted my solution.
<?php
$stdin = fopen('php://stdin', 'r');
$testcase = fgets($stdin);
$n=1;
while($n<=$testcase){
$start = fgets($stdin);
$end=fgets($stdin);
if($start==1) {
$start=2;
}
for($i=$start;$i<$end;$i++){
$flag=0;
for($j=2;$j<$i;$j++){
if($i%$j==0){
$flag=1;
break;
}
}
if($flag==0){
echo $i."\n";
}
}
$n++;
}
fclose($stdin);
?>
Please help me out, I'm stuck with time limit exceeded error and please explain why I'm getting this error. In my local version it shows the correct answer.

Answer 1

Your solution is too slow. Try a slightly modified Sieve of Eratosthenes. The modification should allow your sieve to work only in the [start, end] interval.

Answer 2

In the first for loop, instead for looping all the numbers, you can loop only the odd numbers since other than 2 all the even numbers can never be prime.
you can use $i+=2 in first for loop. this could help you reduce some unnecessary looping.
Update 1:
Also inside second for loop, instead of finding modulo will all the numbers, you could just store the calculated prime numbers in an array and check whether the $i % calculated prime numbers == 0 instead of $i%$j