gmp_prob_prime

    (PHP 4 >= 4.0.4, PHP 5, PHP 7, PHP 8)

    gmp_prob_prime — Check if number is "probably prime"

    Description

    gmp_prob_prime(GMP|int|string $num, int $repetitions = 10): int

    The function uses Miller-Rabin's probabilistic test to check if a number is a prime.

    Parameters

    num

    The number being checked as a prime.

    A GMP object, an int or a numeric string.

    repetitions

    Reasonable values of repetitions vary from 5 to 10 (default being 10); a higher value lowers the probability for a non-prime to pass as a "probable" prime.

    A GMP object, an int or a numeric string.

    Return Values

    If this function returns 0, num is definitely not prime. If it returns 1, then num is "probably" prime. If it returns 2, then num is surely prime.

    Examples

    Example #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";
    ?>

    The above example will output:

    0
1
2

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    User Contributed Notes 1 note

    up
    3
    florin dot ciuica at yahoo dot com
    10 years ago
    <?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
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