# BN_generate_prime

## 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(3).