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BN_generate_prime(3)                OpenSSL               BN_generate_prime(3)

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

       libcrypto, -lcrypto

        #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);

        #define BN_GENCB_set_old(gencb, callback, cb_arg) ...

        #define BN_GENCB_set(gencb, callback, cb_arg) ...


        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 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.

       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.

       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

       BN_generate_prime() returns the prime number on success, NULL

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

       The error codes can be obtained by ERR_get_error(3).

       openssl_bn(3), ERR_get_error(3), openssl_rand(3)

       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

1.0.2k                            2016-10-14              BN_generate_prime(3)