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 string that can be interpreted as a number following the same logic as if the string was used in gmp_init() with automatic base detection (i.e. when base is equal to 0).

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 string that can be interpreted as a number following the same logic as if the string was used in gmp_init() with automatic base detection (i.e. when base is equal to 0).

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

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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