gmp_prob_prime
(PHP 4 >= 4.0.4, PHP 5)
gmp_prob_prime — Check if number is "probably prime"
Описание
The function uses Miller-Rabin's probabilistic test to check if a number is a prime.
Список параметров
- a
-
The number being checked as a prime.
It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.
- reps
-
Reasonable values of reps vary from 5 to 10 (default being 10); a higher value lowers the probability for a non-prime to pass as a "probable" prime.
It can be either a GMP number resource, or a numeric string given that it is possible to convert the latter to a number.
Возвращаемые значения
If this function returns 0, a is definitely not prime. If it returns 1, then a is "probably" prime. If it returns 2, then a is surely prime.
Примеры
Пример #1 gmp_prob_prime() example
<?php
// definitely not a prime
echo gmp_prob_prime("6") . "\n";
// probably a prime
echo gmp_prob_prime("1111111111111111111") . "\n";
// definitely a prime
echo gmp_prob_prime("11") . "\n";
?>
Результат выполнения данного примера:
0 1 2
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- gmp_abs
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Коментарии
<?php
$max = 2147483647;
$primesFound = 0;
$probablePrimes = 0;
for ($x = 1; $x <= $max; $x++) {
$primeStatus = gmp_prob_prime($x);
if ($primeStatus == 1) {
$probablePrimes++;
} else if ($primeStatus == 2) {
$primesFound++;
}
}
echo "Total primes found: " . $primesFound . " between 1 and " . $max . ". Probable primes in this interval: " . $probablePrimes;
?>
Based on that the following results were obtained:
1 - 100000 - certain primes found: 9592, probable: 0
1 - 1000000 - certain primes found: 78498, probable: 0
1 - 10000000 - certain primes found: 78498, probable: 586081
1 - 100000000 - certain primes found: 78498, probable: 5682957
1 - 1000000000 - certain primes found: 78498, probable: 50769036
1 - 2147483647 - certain primes found: 78498, probable: 105019067