# BN_generate_prime

NAME
SYNOPSIS
DESCRIPTION
RETURN VALUES
HISTORY

## NAME

 BN_generate_prime, BN_is_prime, BN_is_prime_fasttest − generate primes and test for primality

## SYNOPSIS

 ``` #include ``` ``` BIGNUM *BN_generate_prime(BIGNUM *ret, int num, int safe, BIGNUM *add, BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg); ``` ``` int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg); ``` ``` int BN_is_prime_fasttest(const BIGNUM *a, int checks, void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg, int do_trial_division); ```

## DESCRIPTION

 BN_generate_prime() generates a pseudo-random prime number of num bits. If ret is not NULL, it will be used to store the number. If callback is not NULL, it is called as follows:
 • callback(0, i, cb_arg) is called after generating the i-th potential prime number. • While the number is being tested for primality, callback(1, j, cb_arg) is called as described below. • When a prime has been found, callback(2, i, cb_arg) is called.
 The prime may have to fulfill additional requirements for use in Diffie-Hellman key exchange: If add is not NULL , the prime will fulfill the condition p % add == rem (p % add == 1 if rem == NULL ) in order to suit a given generator. If safe is true, it will be a safe prime (i.e. a prime p so that (p-1)/2 is also prime). The PRNG must be seeded prior to calling BN_generate_prime(). The prime number generation has a negligible error probability. BN_is_prime() and BN_is_prime_fasttest() test if the number a is prime. The following tests are performed until one of them shows that a is composite; if a passes all these tests, it is considered prime. BN_is_prime_fasttest(), when called with do_trial_division == 1, first attempts trial division by a number of small primes; if no divisors are found by this test and callback is not NULL , callback(1, −1, cb_arg) is called. If do_trial_division == 0, this test is skipped. Both BN_is_prime() and BN_is_prime_fasttest() perform a Miller-Rabin probabilistic primality test with checks iterations. If checks == BN_prime_check, a number of iterations is used that yields a false positive rate of at most 2^−80 for random input. If callback is not NULL , callback(1, j, cb_arg) is called after the j-th iteration (j = 0, 1, ...). ctx is a pre-allocated BN_CTX (to save the overhead of allocating and freeing the structure in a loop), or NULL .

## RETURN VALUES

 BN_generate_prime() returns the prime number on success, NULL otherwise. BN_is_prime() returns 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^checks, and −1 on error. The error codes can be obtained by ERR_get_error(3).