

o  BN_GENCB_call(cb, 0, i) is called after generating the ith potential prime number. 
o  While the number is being tested for primality, BN_GENCB_call(cb, 1, j) is called as described below. 
o  When a prime has been found, BN_GENCB_call(cb, 2, i) is called. 
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 (p1)/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 MillerRabin 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 jth iteration (j = 0, 1, ...). ctx is a preallocated 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(3).
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);
bn(3), ERR_get_error(3), rand(3)
BN_GENCB_new(), BN_GENCB_free(), and BN_GENCB_get_arg() were added in OpenSSL 1.1.0
1.1.0pre3  BN_GENERATE_PRIME (3)  20160215 
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