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BN_generate_prime(3)                OpenSSL               BN_generate_prime(3)

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

       libcrypto, -lcrypto

        #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);

       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:

       o   callback(0, i, cb_arg) is called after generating the i-th
           potential prime number.

       o   While the number is being tested for primality, callback(1, j,
           cb_arg) is called as described below.

       o   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

       BN_generate_prime() returns the prime number on success, NULL

       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).

       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

1.0.1u                            2009-07-19              BN_generate_prime(3)