### NAME

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

### SYNOPSIS

#include <openssl/bn.h> 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_checks**, 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().

### SEE ALSO

### HISTORY

The **cb_arg** arguments to BN_generate_prime() and to BN_is_prime() were added in SSLeay 0.9.0. The **ret** argument to BN_generate_prime() was added in SSLeay 0.9.1. BN_is_prime_fasttest() was added in OpenSSL 0.9.5.