Percent Chance of a New Mersenne Prime Being Found in 2023

[chalsall]

Originally Posted by storm5510

Umm, no! Perhaps by the end of 2024, maybe.

Based on what knowledge?

[storm5510]

Originally Posted by chalsall

Based on what knowledge?

History. Four found in the past decade. The last one found in 2018.

Common sense. No optimism nor pessimism.

[slandrum]

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.

[chalsall]

Originally Posted by slandrum

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.

IMHO, exactly correct.

[mathwiz]

Originally Posted by storm5510

History. Four found in the past decade. The last one found in 2018.

Common sense. No optimism nor pessimism.

"If I just flipped 4 heads with a fair coin, common sense says I'm guaranteed to get tails on the next flip!"

Wrong. Flip 5 is independent of all the others, and is thus p=0.5 heads, p=0.5 tails.

[retina]

Common sense is not a substitute for understanding.

[storm5510]

Originally Posted by slandrum

...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)...

I agree, and stand corrected.

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.

[Andrew Usher]

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!)