BN_generate_prime_ex, BN_is_prime_ex, BN_is_prime_fasttest_ex, BN_GENCB_call, BN_GENCB_new, BN_GENCB_free, BN_GENCB_set_old, BN_GENCB_set, BN_GENCB_get_arg, BN_generate_prime, BN_is_prime, BN_is_prime_fasttest - generate primes and test for primality

```
#include <openssl/bn.h>
int BN_generate_prime_ex(BIGNUM *ret,int bits,int safe, const BIGNUM *add,
const BIGNUM *rem, BN_GENCB *cb);
int BN_is_prime_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx, BN_GENCB *cb);
int BN_is_prime_fasttest_ex(const BIGNUM *p,int nchecks, BN_CTX *ctx,
int do_trial_division, BN_GENCB *cb);
int BN_GENCB_call(BN_GENCB *cb, int a, int b);
BN_GENCB *BN_GENCB_new(void);
void BN_GENCB_free(BN_GENCB *cb);
void BN_GENCB_set_old(BN_GENCB *gencb,
void (*callback)(int, int, void *), void *cb_arg);
void BN_GENCB_set(BN_GENCB *gencb,
int (*callback)(int, int, BN_GENCB *), void *cb_arg);
void *BN_GENCB_get_arg(BN_GENCB *cb);
```

Deprecated:

```
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);
```

BN_generate_prime_ex() generates a pseudo-random prime number of at least bit length **bits**. If **ret** is not **NULL**, it will be used to store the number.

If **cb** is not **NULL**, it is used as follows:

**BN_GENCB_call(cb, 0, i)**is called after generating the i-th potential prime number.While the number is being tested for primality,

**BN_GENCB_call(cb, 1, j)**is called as described below.When a prime has been found,

**BN_GENCB_call(cb, 2, i)**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_ex(). The prime number generation has a negligible error probability.

BN_is_prime_ex() and BN_is_prime_fasttest_ex() test if the number **p** is prime. The following tests are performed until one of them shows that **p** is composite; if **p** passes all these tests, it is considered prime.

BN_is_prime_fasttest_ex(), 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 **cb** is not **NULL**, **BN_GENCB_call(cb, 1, -1)** is called. If **do_trial_division == 0**, this test is skipped.

Both BN_is_prime_ex() and BN_is_prime_fasttest_ex() perform a Miller-Rabin probabilistic primality test with **nchecks** iterations. If **nchecks == BN_prime_checks**, a number of iterations is used that yields a false positive rate of at most 2^-80 for random input.

If **cb** is not **NULL**, **BN_GENCB_call(cb, 1, j)** 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**.

BN_GENCB_call calls the callback function held in the **BN_GENCB** structure and passes the ints **a** and **b** as arguments. There are two types of **BN_GENCB** structure that are supported: "new" style and "old" style. New programs should prefer the "new" style, whilst the "old" style is provided for backwards compatibility purposes.

A BN_GENCB structure should be created through a call to BN_GENCB_new, and freed through a call to BN_GENCB_free.

For "new" style callbacks a BN_GENCB structure should be initialised with a call to BN_GENCB_set(), where **gencb** is a **BN_GENCB ***, **callback** is of type **int (*callback)(int, int, BN_GENCB *)** and **cb_arg** is a **void ***. "Old" style callbacks are the same except they are initialised with a call to BN_GENCB_set_old() and **callback** is of type **void (*callback)(int, int, void *)**.

A callback is invoked through a call to **BN_GENCB_call**. This will check the type of the callback and will invoke **callback(a, b, gencb)** for new style callbacks or **callback(a, b, cb_arg)** for old style.

It is possible to obtained the argument associated with a BN_GENCB structure (set via a call to BN_GENCB_set or BN_GENCB_set_old) using BN_GENCB_get_arg.

BN_generate_prime (deprecated) works in the same way as BN_generate_prime_ex but expects an old style callback function directly in the **callback** parameter, and an argument to pass to it in the **cb_arg**. Similarly BN_is_prime and BN_is_prime_fasttest are deprecated and can be compared to BN_is_prime_ex and BN_is_prime_fasttest_ex respectively.

BN_generate_prime_ex() return 1 on success or 0 on error.

BN_is_prime_ex(), BN_is_prime_fasttest_ex(), BN_is_prime() and BN_is_prime_fasttest() return 0 if the number is composite, 1 if it is prime with an error probability of less than 0.25^**nchecks**, and -1 on error.

BN_generate_prime() returns the prime number on success, **NULL** otherwise.

BN_GENCB_new returns a pointer to a BN_GENCB structure on success, or **NULL** otherwise.

BN_GENCB_get_arg returns the argument previously associated with a BN_GENCB structure.

Callback functions should return 1 on success or 0 on error.

The error codes can be obtained by ERR_get_error.

As of OpenSSL 1.1.0 it is no longer possible to create a BN_GENCB structure directly, as in:

` BN_GENCB callback;`

Instead applications should create a BN_GENCB structure using BN_GENCB_new:

```
BN_GENCB *callback;
callback = BN_GENCB_new();
if(!callback) /* handle error */
...
BN_GENCB_free(callback);
```

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. BN_GENCB_new, BN_GENCB_free and BN_GENCB_get_arg were added in OpenSSL 1.1.0