The idea is that with 2n you always go down to one. But for some values of that happene to be messene prime + 1,they cannot be reached by 3*(whatever) + 1, only

The idea is that with 2n you always go down to one. But for some values of that happene to be messene prime + 1,they cannot be reached by 3*(whatever) + 1, only from above. So focusing on the points that this conjecture reaches only that way, can probably give a faster way to find messene primes.