It's a Mersenne prime. I was curious so looked at the list of numbers that have been the largest known prime. It turns out that the last time the largest known prime was not a Mersenne prime was in 1989. That was 391581 x 2^216193 - 1 and had 65087 digits.
There have been 19 largest known primes since then and all are Mersenne primes.
Out of the 20 largest known primes, 12 are Mersenne primes. The ones that aren't are at positions 8, 9, 12, 14, 16, 18, 19, and 20.
In this 2 days it changed from "probable" to "confirmed". Anyway, I don't know if there is something new to say. Anyway^2, this video explain a lot of details about how they found the number that were not explained in the old post. (New probabilistic algorithm, then confirm with the (old?) deterministic algorithm, use a distributed "cloud" of computer of volunteers to make all the tests).
PS: [spoiler alert?] After watching the video I realized the background is real. I was expecting a joke or something. I'm too used to Zoom and fake backgrounds :( .
But if there is a practical application to very large primes: I don’t know. 40 million digits sounds very inefficient unless you always operate in sub-groups.
It's a Mersenne prime. I was curious so looked at the list of numbers that have been the largest known prime. It turns out that the last time the largest known prime was not a Mersenne prime was in 1989. That was 391581 x 2^216193 - 1 and had 65087 digits.
There have been 19 largest known primes since then and all are Mersenne primes.
Out of the 20 largest known primes, 12 are Mersenne primes. The ones that aren't are at positions 8, 9, 12, 14, 16, 18, 19, and 20.
Discussion (355 points, 2 days ago, 118 comments) https://news.ycombinator.com/item?id=41858024
In this 2 days it changed from "probable" to "confirmed". Anyway, I don't know if there is something new to say. Anyway^2, this video explain a lot of details about how they found the number that were not explained in the old post. (New probabilistic algorithm, then confirm with the (old?) deterministic algorithm, use a distributed "cloud" of computer of volunteers to make all the tests).
PS: [spoiler alert?] After watching the video I realized the background is real. I was expecting a joke or something. I'm too used to Zoom and fake backgrounds :( .
Is there any practical application of a new prime number?
Prime numbers with practical applications do get discovered. Most notably, I suppose: 2^64 - 2^32 + 1:
https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-fo...
There are annual prizes on performing certain computations efficiently in prime fields for this prime:
https://www.zprize.io/
But if there is a practical application to very large primes: I don’t know. 40 million digits sounds very inefficient unless you always operate in sub-groups.
"prime number digits" -> "video"
thank you, i hate it
Bad take. The Stand-Up Maths channel is great.