On September 22, 2017 our data on number of steps in Collatz sequence for Mersenne primes were included in OEIS as an addition to A181777. Prior to this A181777 contained information up to the 42nd Mersenne prime only.
The data on required number of steps to reach 1 for the 43rd, 44th and 45th Mersenne primes were included immediately, whereas the data on the 46th, 47th, 48th and 49th known Mersenne primes will be included in the future once mathematicians confirm currently provisional ranking of these primes as well as the absence of other presently unknown Mersenne primes between 45th (М37156667) and 49th (М74207281). Such a confirmation may take many years or even decades to come.
Below is a table with our data for all known Mersenne primes starting from the 43rd.
Mp # of steps to 1
As far as we know, full Collatz conjecture statistics for large Mersenne primes has never been published before and none of Mersenne primes above the 47th one (M43112609) has ever been tested for Collatz conjecture confirmation.
We continue to process our results and plan to present most important of them in the future.