gmp_prob_prime

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

gmp_prob_prime — Check if number is "probably prime"

Beschreibung

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.

Parameter-Liste

num

The number being checked as a prime.

Ein GMP-Object, ein Integer oder eine Zeichenkette, die als Zahl interpretiert werden kann, wobei die gleiche Logik gilt, als ob die Zeichenkette in gmp_init() mit automatischer Erkennung der Basis verwendet würde (d. h. wenn base gleich 0 ist).

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.

Rückgabewerte

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.

Beispiele

Beispiel #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";
?>

Das oben gezeigte Beispiel erzeugt folgende Ausgabe:

0
1
2

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User Contributed Notes 1 note

down

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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