/**
* Finds next strong pseudoprime number, following after $num
*
* @param gmp resource $num
* @return gmp resource
* @access public
*/
function nextPrime($num)
{
if (!gmp_cmp(gmp_mod($num, 2), 0)) {
$num = gmp_sub($num, 1);
}
do {
$num = gmp_add($num, 2);
} while (!gmp_prob_prime($num));
return $num;
}
function get_prime_number()
{
$primos = 0;
$numeros = 0;
do {
$aux = gmp_prob_prime($numeros);
if ($aux == 2) {
$primos++;
}
$numeros++;
} while ($primos <= 10001);
return $numeros;
}
protected function calcularPrimo()
{
$x = 0;
$i = 0;
while ($i < 10001) {
if ($this->isImpar($x) || $x == 2) {
if (gmp_prob_prime($x) == 2) {
$primo = $x;
$i++;
}
}
$x++;
}
return $primo;
}
/**
* Checks a numer to see if it's prime
*
* Assuming the $t parameter is not set, this function has an error rate of 2**-80. The main motivation for the
* $t parameter is distributability. Math_BigInteger::randomPrime() can be distributed across multiple pageloads
* on a website instead of just one.
*
* @param Math_BigInteger $t
* @return bool
* @access public
* @internal Uses the
* {@link http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test Miller-Rabin primality test}. See
* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=8 HAC 4.24}.
*/
function isPrime($t = false)
{
$length = strlen($this->toBytes());
if (!$t) {
// see HAC 4.49 "Note (controlling the error probability)"
// @codingStandardsIgnoreStart
if ($length >= 163) {
$t = 2;
} else {
if ($length >= 106) {
$t = 3;
} else {
if ($length >= 81) {
$t = 4;
} else {
if ($length >= 68) {
$t = 5;
} else {
if ($length >= 56) {
$t = 6;
} else {
if ($length >= 50) {
$t = 7;
} else {
if ($length >= 43) {
$t = 8;
} else {
if ($length >= 37) {
$t = 9;
} else {
if ($length >= 31) {
$t = 12;
} else {
if ($length >= 25) {
$t = 15;
} else {
if ($length >= 18) {
$t = 18;
} else {
$t = 27;
}
}
}
}
}
}
}
}
}
}
}
// @codingStandardsIgnoreEnd
}
// ie. gmp_testbit($this, 0)
// ie. isEven() or !isOdd()
switch (MATH_BIGINTEGER_MODE) {
case MATH_BIGINTEGER_MODE_GMP:
return gmp_prob_prime($this->value, $t) != 0;
case MATH_BIGINTEGER_MODE_BCMATH:
if ($this->value === '2') {
return true;
}
if ($this->value[strlen($this->value) - 1] % 2 == 0) {
return false;
}
break;
default:
if ($this->value == array(2)) {
return true;
}
if (~$this->value[0] & 1) {
return false;
}
}
static $primes, $zero, $one, $two;
if (!isset($primes)) {
$primes = array(3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997);
if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
for ($i = 0; $i < count($primes); ++$i) {
$primes[$i] = new Math_BigInteger($primes[$i]);
}
}
$zero = new Math_BigInteger();
$one = new Math_BigInteger(1);
$two = new Math_BigInteger(2);
}
if ($this->equals($one)) {
return false;
}
// see HAC 4.4.1 "Random search for probable primes"
if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
foreach ($primes as $prime) {
list(, $r) = $this->divide($prime);
if ($r->equals($zero)) {
return $this->equals($prime);
}
}
} else {
$value = $this->value;
foreach ($primes as $prime) {
list(, $r) = $this->_divide_digit($value, $prime);
if (!$r) {
return count($value) == 1 && $value[0] == $prime;
}
}
}
$n = $this->copy();
$n_1 = $n->subtract($one);
$n_2 = $n->subtract($two);
$r = $n_1->copy();
$r_value = $r->value;
// ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
if (MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH) {
$s = 0;
// if $n was 1, $r would be 0 and this would be an infinite loop, hence our $this->equals($one) check earlier
while ($r->value[strlen($r->value) - 1] % 2 == 0) {
$r->value = bcdiv($r->value, '2', 0);
++$s;
}
} else {
for ($i = 0, $r_length = count($r_value); $i < $r_length; ++$i) {
$temp = ~$r_value[$i] & 0xffffff;
for ($j = 1; $temp >> $j & 1; ++$j) {
}
if ($j != 25) {
break;
}
}
$s = 26 * $i + $j - 1;
$r->_rshift($s);
}
for ($i = 0; $i < $t; ++$i) {
$a = $this->random($two, $n_2);
$y = $a->modPow($r, $n);
if (!$y->equals($one) && !$y->equals($n_1)) {
for ($j = 1; $j < $s && !$y->equals($n_1); ++$j) {
$y = $y->modPow($two, $n);
if ($y->equals($one)) {
return false;
}
}
if (!$y->equals($n_1)) {
return false;
}
}
}
return true;
}
public function testVerificarNumero2EPrimo()
{
$this->assertEquals(2, gmp_prob_prime(2));
}
$pow1 = gmp_pow("2", 31);
echo gmp_strval($pow1) . "\n";
$pow2 = gmp_pow("0", 0);
echo gmp_strval($pow2) . "\n";
$pow3 = gmp_pow("2", -1);
// Negative exp, generates warning
echo gmp_strval($pow3) . "\n";
// gmp_powm
$pow1 = gmp_powm("2", "31", "2147483649");
echo gmp_strval($pow1) . "\n";
// gmp_prob_prime
echo gmp_prob_prime("6") . "\n";
// definitely not a prime
echo gmp_prob_prime("1111111111111111111") . "\n";
// probably a prime
echo gmp_prob_prime("11") . "\n";
// definitely a prime
// gmp_random -- not implemented
// gmp_scan0
// "0" bit is found at position 3. index starts at 0
$s1 = gmp_init("10111", 2);
echo gmp_scan0($s1, 0) . "\n";
// "0" bit is found at position 7. index starts at 5
$s2 = gmp_init("101110000", 2);
echo gmp_scan0($s2, 5) . "\n";
// gmp_scan1
// "0" bit is found at position 3. index starts at 0
$s1 = gmp_init("01000", 2);
echo gmp_scan1($s1, 0) . "\n";
// "0" bit is found at position 7. index starts at 5
$s2 = gmp_init("01000001111", 2);
public static function is_prime($n)
{
if (extension_loaded('gmp') && USE_EXT == 'GMP') {
return gmp_prob_prime($n);
} elseif (extension_loaded('bcmath') && USE_EXT == 'BCMATH') {
self::$miller_rabin_test_count = 0;
$t = 40;
$k = 0;
$m = bcsub($n, 1);
while (bcmod($m, 2) == 0) {
$k = bcadd($k, 1);
$m = bcdiv($m, 2);
}
for ($i = 0; $i < $t; $i++) {
$a = bcmath_Utils::bcrand(1, bcsub($n, 1));
$b0 = self::modular_exp($a, $m, $n);
if ($b0 != 1 && $b0 != bcsub($n, 1)) {
$j = 1;
while ($j <= $k - 1 && $b0 != bcsub($n, 1)) {
$b0 = self::modular_exp($b0, 2, $n);
if ($b0 == 1) {
self::$miller_rabin_test_count = $i + 1;
return false;
}
$j++;
}
if ($b0 != bcsub($n, 1)) {
self::$miller_rabin_test_count = $i + 1;
return false;
}
}
}
return true;
} else {
throw new ErrorException("Please install BCMATH or GMP");
}
}
<?php
var_dump(gmp_prob_prime(10));
var_dump(gmp_prob_prime("7"));
var_dump(gmp_prob_prime(17));
var_dump(gmp_prob_prime(-31));
var_dump(gmp_prob_prime("172368715471481723"));
var_dump(gmp_prob_prime(10));
var_dump(gmp_prob_prime("7"));
var_dump(gmp_prob_prime(17));
var_dump(gmp_prob_prime(-31));
var_dump(gmp_prob_prime("172368715471481723"));
for ($i = -1; $i < 12; $i++) {
var_dump(gmp_prob_prime(773 * $i - $i * 7 - 1, $i));
$n = gmp_init("23476812735411");
var_dump(gmp_prob_prime(gmp_add($n, $i - 1), $i));
}
$n = gmp_init("19481923");
var_dump(gmp_prob_prime($n));
$n = gmp_init(0);
var_dump(gmp_prob_prime($n));
var_dump(gmp_prob_prime());
var_dump(gmp_prob_prime(array()));
echo "Done\n";
public function isPrime($t = false)
{
$length = strlen($this->toBytes());
if (!$t) {
if (163 <= $length) {
$t = 2;
} else {
if (106 <= $length) {
$t = 3;
} else {
if (81 <= $length) {
$t = 4;
} else {
if (68 <= $length) {
$t = 5;
} else {
if (56 <= $length) {
$t = 6;
} else {
if (50 <= $length) {
$t = 7;
} else {
if (43 <= $length) {
$t = 8;
} else {
if (37 <= $length) {
$t = 9;
} else {
if (31 <= $length) {
$t = 12;
} else {
if (25 <= $length) {
$t = 15;
} else {
if (18 <= $length) {
$t = 18;
} else {
$t = 27;
}
}
}
}
}
}
}
}
}
}
}
}
switch (MATH_BIGINTEGER_MODE) {
case MATH_BIGINTEGER_MODE_GMP:
return gmp_prob_prime($this->value, $t) != 0;
case MATH_BIGINTEGER_MODE_BCMATH:
if ($this->value === '2') {
return true;
}
if ($this->value[strlen($this->value) - 1] % 2 == 0) {
return false;
}
break;
default:
if ($this->value == array(2)) {
return true;
}
if (~$this->value[0] & 1) {
return false;
}
}
static $primes;
static $zero;
static $one;
static $two;
if (!isset($primes)) {
$primes = array(3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997);
if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
for ($i = 0; $i < count($primes); ++$i) {
$primes[$i] = new Math_BigInteger($primes[$i]);
}
}
$zero = new Math_BigInteger();
$one = new Math_BigInteger(1);
$two = new Math_BigInteger(2);
}
if ($this->equals($one)) {
return false;
}
if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
foreach ($primes as $prime) {
list(, $r) = $this->divide($prime);
if ($r->equals($zero)) {
return $this->equals($prime);
}
}
} else {
$value = $this->value;
foreach ($primes as $prime) {
list(, $r) = $this->_divide_digit($value, $prime);
if (!$r) {
return count($value) == 1 && $value[0] == $prime;
}
}
}
$n = $this->copy();
$n_1 = $n->subtract($one);
$n_2 = $n->subtract($two);
$r = $n_1->copy();
$r_value = $r->value;
if (MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH) {
$s = 0;
while ($r->value[strlen($r->value) - 1] % 2 == 0) {
$r->value = bcdiv($r->value, '2', 0);
++$s;
}
} else {
$i = 0;
for ($r_length = count($r_value); $i < $r_length; ++$i) {
$temp = ~$r_value[$i] & 16777215;
for ($j = 1; $temp >> $j & 1; ++$j) {
}
if ($j != 25) {
break;
}
}
$s = 26 * $i + $j - 1;
$r->_rshift($s);
}
for ($i = 0; $i < $t; ++$i) {
$a = $this->random($two, $n_2);
$y = $a->modPow($r, $n);
if (!$y->equals($one) && !$y->equals($n_1)) {
for ($j = 1; !$y->equals($n_1); ++$j) {
$y = $y->modPow($two, $n);
if ($y->equals($one)) {
return false;
}
}
if (!$y->equals($n_1)) {
return false;
}
}
}
return true;
}
/**
* Generates prime number with length $bits_cnt
* using $random_generator as random generator function.
*
* @param int $bits_cnt
* @param string $rnd_generator
* @access public
*/
function getPrime($bits_cnt, $random_generator)
{
$bytes_n = intval($bits_cnt / 8);
$bits_n = $bits_cnt % 8;
do {
$str = '';
for ($i = 0; $i < $bytes_n; $i++) {
$str .= chr(call_user_func($random_generator) & 0xff);
}
$n = call_user_func($random_generator) & 0xff;
$n |= 0x80;
$n >>= 8 - $bits_n;
$str .= chr($n);
$num = $this->bin2int($str);
// search for the next closest prime number after [$num]
if (!gmp_cmp(gmp_mod($num, '2'), '0')) {
$num = gmp_add($num, '1');
}
while (!gmp_prob_prime($num)) {
$num = gmp_add($num, '2');
}
} while ($this->bitLen($num) != $bits_cnt);
return $num;
}
public function isPrime($number)
{
return gmp_prob_prime($number) ? true : false;
}
/**
* @param int $number
*/
public static function isPrime($number)
{
// Uses Miller-Rabin's probabilistic test
// https://en.wikipedia.org/wiki/Miller-Rabin_primality_test
return gmp_prob_prime($number) !== 0;
}
/**
* {@inheritDoc}
* @see \Mdanter\Ecc\MathAdapterInterface::isPrime()
*/
public function isPrime($n)
{
$prob = gmp_prob_prime(gmp_init($n, 10));
if ($prob > 0) {
return true;
}
return false;
}
# numero_primo
<?php
//exemplo com o numero 10.
$numero = 10;
if (gmp_prob_prime($numero)) {
print 'É primo';
} else {
print 'Não é primo';
}
<?php
/**
*
* @Author: Marcelo C Menezes
* https://github.com/marcelocmenezes
*
* Etapa 1
*
*/
$contador = 0;
for ($i = 2; $i <= 1000000; $i++) {
if (gmp_prob_prime($i) == 2) {
$contador++;
if ($contador == 10001) {
echo $i;
}
}
}
<?php
$i = 600851475143.0;
$x = 1;
while ($x <= $i) {
if ($i % $x == 0) {
$factor = $i / $x;
if (gmp_prob_prime($factor) == 2) {
echo $factor;
break;
}
}
$x++;
}
