20230621, 00:36  #45 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{2}·5·571 Posts 

20230621, 12:17  #46 
Random Account
Aug 2009
Oceanus Procellarum
101111000111_{2} Posts 

20230621, 16:51  #47 
Jan 2021
California
2×7×41 Posts 
Having spent a period of my live as a professional gambler and paying attention to the numbers, one thing you learn is that events that are (close enough to) random don't come "due". If you have a coin that's fair, it's 50/50 to come out heads on the next flip, regardless of what happened on the last flip, or the last 10 or 100 or 100000. Similarly in the search for Mersenne primes, we have no idea how long gaps can be. Even if we know how the distribution should be statistically, when you hit a long dry spell, the next number tested is still no more or less likely to be the one than the one before it (except for the general trend that as the numbers get larger they are less likely to be prime).
From this perspective, the fact that no MP have been discovered since 2018 is largely irrelevant, and not useful in a predictive sense for when the next one will be discovered. 
20230621, 17:48  #48 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{2}×5×571 Posts 

20230622, 00:28  #49  
Mar 2019
18A_{16} Posts 
Quote:
Wrong. Flip 5 is independent of all the others, and is thus p=0.5 heads, p=0.5 tails. 

20230622, 02:13  #50 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
15310_{8} Posts 
Common sense is not a substitute for understanding.

20230622, 14:26  #51  
Random Account
Aug 2009
Oceanus Procellarum
3^{2}×5×67 Posts 
Quote:
The distribution is not predictable unlike multiples of 2. e.g. 2, 4, 8, 16, and so on. Charted as a function of time, a line would rise and fall based on the varying intervals between finds. 

20230624, 12:24  #52 
Dec 2022
2×3×7×13 Posts 
Probability has no memory, to state it concisely. Hence the ubiquity and utility of the Poisson distribution. (And of course you meant powers of 2, not multiples, though the point would have been the same!)

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