Best way to seed mt19937_64 for Monte Carlo simulations

Use std::random_device to generate the seed. It’ll provide non-deterministic random numbers, provided your implementation supports it. Otherwise it’s allowed to use some other random number engine.

std::mt19937_64 prng;
seed = std::random_device{}();
prng.seed(seed);

operator() of std::random_device returns an unsigned int, so if your platform has 32-bit ints, and you want a 64-bit seed, you’ll need to call it twice.

std::mt19937_64 prng;
std::random_device device;
seed = (static_cast<uint64_t>(device()) << 32) | device();
prng.seed(seed);

Another available option is using std::seed_seq to seed the PRNG. This allows the PRNG to call seed_seq::generate, which produces a non-biased sequence over the range [0 ≤ i < 2³²), with an output range large enough to fill its entire state.

std::mt19937_64 prng;
std::random_device device;
std::seed_seq seq{device(), device(), device(), device()};
prng.seed(seq);

I’m calling the random_device 4 times to create a 4 element initial sequence for seed_seq. However, I’m not sure what the best practice for this is, as far as length or source of elements in the initial sequence is concerned.