In a footnote to the list of known Mersenne prime numbers which can be found [here](https://www.mersenne.org/primes/), we read that the "ranking" therein is a provisional one since not all possible exponents between $37 \, 156 \, 667$ and $77 \, 232 \, 917$ have been eliminated/tested.


If we may infer from this that the individual(s) who recently found the largest known prime number had not previously discarded (quite understandably!) the possible compositeness of the $\pi(77 \, 232 \, 917)-\pi(74 \, 207 \, 281) - 1 = 166 \, 801$ members of the set $$\{M\_{p} \colon p \in (74 \, 207 \, 281, 77 \, 232 \, 917), p \mbox{ is a prime number}\},$$ do we know what it was that prompted them to try their hand at establishing the primality of *the very specific* Mersenne number $M\_{77 \, 232 \, 917}$ ?


Clearly enough, an analogous question can be formulated regarding the discovery of the 46th, 47th, 48th, and 49th known Mersenne prime numbers. If you know the answer to any of those allied questions, do not hesitate to enter it below (it might shed light on the case of the 50th known Mersenne prime). 


Thanks in advance for your knowledgeable replies.



Question on the 50th (known) Mersenne prime number
As Jan Grabowski notes, all the primes that you mention have been discovered by GIMPS. GIMPS draws a distinction between *testing* and *double-checking*. When a Lucas–Lehmer test is performed on a Mersenne number and delivers a verdict that the number is prime, the computation is immediately verified. Only after the verification checks out is it announced that a new prime has been discovered. However, if the verdict of the LL test is that the number is composite, the double-checking may not be performed immediately. There is a rather complicated set of [assignment rules](https://www.mersenne.org/thresholds/) that determines what computations are to be done next on which computers.


Almost all the Mersenne numbers up to the current largest known Mersenne prime have been tested at least once (the small number of exceptions is due to the nature of distributed computing). However, not all the composites have been double-checked. GIMPS does not declare a range to be prime-free until all the composites in that range have been double-checked.


