diff --git a/doc/man3/BN_generate_prime.pod b/doc/man3/BN_generate_prime.pod
index 31fbc1ffa1743f193603a82928e8ef0edf78eceb..d26e0a99c898ffb8ad2d20f66f73b7453d3571a1 100644
--- a/doc/man3/BN_generate_prime.pod
+++ b/doc/man3/BN_generate_prime.pod
@@ -52,7 +52,9 @@ Deprecated:
 
 BN_generate_prime_ex() generates a pseudo-random prime number of
 at least bit length B<bits>. The returned number is probably prime
-with a negligible error.
+with a negligible error. If B<add> is B<NULL> the returned prime
+number will have exact bit length B<bits> with the top most two
+bits set.
 
 If B<ret> is not B<NULL>, it will be used to store the number.
 
@@ -89,7 +91,9 @@ If B<add> is not B<NULL>, the prime will fulfill the condition p % B<add>
 generator.
 
 If B<safe> is true, it will be a safe prime (i.e. a prime p so
-that (p-1)/2 is also prime).
+that (p-1)/2 is also prime). If B<safe> is true, and B<rem> == B<NULL>
+the condition will be p % B<add> == 3.
+It is recommended that B<add> is a multiple of 4.
 
 The random generator must be seeded prior to calling BN_generate_prime_ex().
 If the automatic seeding or reseeding of the OpenSSL CSPRNG fails due to