function q46()
{
$number = 1;
while (true) {
$number += 2;
if (IntegerFactorization::isPrime($number)) {
continue;
}
// Try squares in ascending order and test whether the difference between the current number
// and this double square is a prime
// If we find a working combination (prime + double square), then this number is not the one we're looking for
// If we find no combination of a square + prime up to the number, then it is the number we are looking for
$found = false;
$square = 1;
$doubleSquare = 2 * $square * $square;
while ($doubleSquare <= $number) {
$complement = $number - $doubleSquare;
if (IntegerFactorization::isPrime($complement)) {
$found = true;
break;
}
++$square;
$doubleSquare = 2 * $square * $square;
}
if (!$found) {
break;
}
}
return $number;
}
/**
* @param int $n
* @return bool
*/
public static function isTruncatablePrime($n)
{
if (!IntegerFactorization::isPrime($n)) {
return false;
}
$stringRepresentation = (string) $n;
$stringRepresentationLength = strlen($stringRepresentation);
// Left to right
for ($i = 1; $i < $stringRepresentationLength; ++$i) {
$number = substr($stringRepresentation, $i);
if (!IntegerFactorization::isPrime($number)) {
return false;
}
}
// Right to left
for ($i = 1; $i < $stringRepresentationLength; ++$i) {
$number = substr($stringRepresentation, 0, $i);
if (!IntegerFactorization::isPrime($number)) {
return false;
}
}
return true;
}
