关于已发现最大与第二大梅森素数间是否存在未发现梅森素数的技术问询

Hey there! Let's dive into your question about the gap between the second-largest and newly discovered largest Mersenne primes.

First, let's recap the key known details:

• 18 days ago, Luke Durant uncovered a new Mersenne prime: $2^{136,279,841} - 1$
• The second-largest known Mersenne prime was found way back on December 7, 2018: $2^{82,589,933} - 1$

There's a visualization that maps each discovered Mersenne prime's discovery date to the size of its exponent. Looking at this plot, you can see a clear, unbroken gap between the exponents 82,589,933 and 136,279,841—no known primes fill that space right now.

This gap is what's got you curious, right? You're wondering: is it really true that there are no undiscovered Mersenne primes between $2^{82,589,933} - 1$ and $2^{136,279,841} - 1$? If these two end up being consecutive Mersenne primes (with no missing ones in between), that would open up some really interesting questions about how future Mersenne primes might be distributed.

备注：内容来源于stack exchange，提问作者user1380196