Let's say you have to find if there is a prime gap of 30 between 1000000 and 1000040, you have calculated all the prime numbers until 1000040 instead of only checking which of those 40 numbers were primes, I don't think that's ok.

Hint: you need to multiply two numbers to get a number. Let's say you're checking if 2 * 13 = 26 is prime: By the you get to "13 is a divisor by 26", you'd already have checked "2 is a divisor by 26" ;-)

Half is too much, you need a better estimate ;-)

Checking for primality is expensive (in time), so why are you calculating all primes between 1 (that's not a prime number btw) and n?

For string that could be in multiple lines you need \A/\Z instead to match the entire string:

https://stackoverflow.com/questions/4250062/what-is-the-difference-between-and-a-and-z-in-regex

    a1           a2
[2, 2, 3] -> [9, 4, 4] // ok
[2, 3, 3] -> [4, 4, 9] // not ok
[2, 2, 2] -> [4, 4, 9] // not ok either

That's what same multiplicity means, your code only checks if any value of a2 is the square of all values of a1.

Use this to print your arrays:

  echo "Array a1: ";
  print_r($a1);
  echo "Array a2: ";
  print_r($a2);
  echo'';

Your code doesn't address the "same multiplicity" condition.