RANDOM mode does not enforce any sequence or minimal number of keys to generate before checking. Each key is generated and checked independently.
The program does not enforce any specific sequence or pattern in the keys it generates. It relies on the randomness of the PRNG to explore the key space uniformly.
The program processes keys in batches of 512 (2 × 256) to optimize performance using AVX2 instructions for hashing.
Progress and elapsed time are not calculated in RANDOM mode.
The speed of 4.6 Mkeys/s per core is achievable with AVX2 optimizations, but it depends on the hardware.
What's the frequency of a single core?
Are you doing affine (not jacobian) batched addition, using the secp256k1_fe_* primitives? And the P (+ - ) Q trick?
That is, if the programm shows 4 M keys second in RND mode, there were generated 4 M keys?