mathematics New highest-known prime number (it's a Mersenne prime, to boot!) and newest known perfect number dropped

[splesh]

The new highest prime number yet discovered was, and only about a week ago, too. This time, it was in San Jose, California, USA, by former NVIDIA employee Luke Durant. As an added bonus, this number is also a so called Mersenne prime, a special subset in the form 2^p - 1. Part of what makes the discovery of the newest known Mersenne prime, which is only the 52nd to date, is that it has along with it the newest known perfect number. A perfect number is one whose divisors sum to the number itself. The classic example of a perfect number is 6, because 1 * 2 * 3 = 6 and 1 + 2 + 3 = 6. Perfect numbers can be written in the form (2^p-1 - 1)(2^p - 1), when the latter term is prime, and this was shown by Euclid in 300 BC. Euclid also famously proved that there are an infinite number of primes. Yet, despite this, the following remain open problems in mathematics: whether there are an infinite number of Mersenne primes, whether there are an infinite number of perfect numbers, and whether or not perfect numbers can be odd. The number Luke Durant about a week ago found can be expressed as 2^136,279,841 - 1, which has more than 41 million decimal digits, and is known as M136279841 (the M standing for Mersenne, and the number for the value of p). This number has in fact, 41,024,320 decimal digits, to be more precise. And that, my friends, is more than 18 million more digits than the 51st mersenne prime, which was found six years ago.

So, it's not like Riemann's hypothesis or P = NP was proved or disproved, but isn't it nice to have some good news every once in awhile?

[Satans Little Helper]

[Dragon]

gotta admire the dedication it takes to find out if 2^136,279,841 - 1 actually is a prime. and this is the awesome type of prime number that creates a Perfect number, holy shit. it's been six years.

i heard a new weird number is on the way

[geosmina]

2 hours ago, splesh said:

The new highest prime number yet discovered was, and only about a week ago, too. This time, it was in San Jose, California, USA, by former NVIDIA employee Luke Durant. As an added bonus, this number is also a so called Mersenne prime, a special subset in the form 2^p - 1. Part of what makes the discovery of the newest known Mersenne prime, which is only the 52nd to date, is that it has along with it the newest known perfect number. A perfect number is one whose divisors sum to the number itself. The classic example of a perfect number is 6, because 1 * 2 * 3 = 6 and 1 + 2 + 3 = 6. Perfect numbers can be written in the form (2^p-1 - 1)(2^p - 1), when the latter term is prime, and this was shown by Euclid in 300 BC. Euclid also famously proved that there are an infinite number of primes. Yet, despite this, the following remain open problems in mathematics: whether there are an infinite number of Mersenne primes, whether there are an infinite number of perfect numbers, and whether or not perfect numbers can be odd. The number Luke Durant about a week ago found can be expressed as 2^136,279,841 - 1, which has more than 41 million decimal digits, and is known as M136279841 (the M standing for Mersenne, and the number for the value of p). This number has in fact, 41,024,320 decimal digits, to be more precise. And that, my friends, is more than 18 million more digits than the 51st mersenne prime, which was found six years ago.

So, it's not like Riemann's hypothesis or P = NP was proved or disproved, but isn't it nice to have some good news every once in awhile?

Nice. Reminds me of this beautiful book called The Computational Beauty of Nature—this book explains why this is important and why it is actually a beautiful thing too...

[auxien]

perfect numbers are even, i’m not sure where you’re getting that perfect number stuff…

the expense of this is interesting as well. it’s a lot of computation, takes a lot of resources to hunt for this which, i’m not saying it should t be done, is kinda just a marker point.

not shitting on anything, this is cool! just weird that at this point the search is just algorithmic chugging.

[Dragon]

1 hour ago, auxien said:

perfect numbers are even, i’m not sure where you’re getting that perfect number stuff…

the expense of this is interesting as well. it’s a lot of computation, takes a lot of resources to hunt for this which, i’m not saying it should t be done, is kinda just a marker point.

not shitting on anything, this is cool! just weird that at this point the search is just algorithmic chugging.

perfect number because a Mersenne prime always has a perfect number baked inside it https://en.m.wikipedia.org/wiki/Mersenne_prime

Quote

Mersenne primes Mp are closely connected to perfect numbers. In the 4th century BC, Euclid proved that if 2p − 1 is prime, then 2p − 1(2p − 1) is a perfect number. In the 18th century, Leonhard Euler proved that, conversely, all even perfect numbers have this form. This is known as the Euclid–Euler theorem. It is unknown whether there are any odd perfect numbers.

btw i didn't see the new numberphile coverage of this. thanks!

[auxien]

47 minutes ago, Dragon said:

perfect number because a Mersenne prime always has a perfect number baked inside it https://en.m.wikipedia.org/wiki/Mersenne_prime

btw i didn't see the new numberphile coverage of this. thanks!

nice, thanks! i’m traveling today & probably didn’t completely read/understand the first post from splesh. cool stuff to see

[splesh]

On 10/26/2024 at 4:28 PM, Dragon said:

gotta admire the dedication it takes to find out if 2^136,279,841 - 1 actually is a prime. and this is the awesome type of prime number that creates a Perfect number, holy shit. it's been six years.

i heard a new weird number is on the way

Sorry to be such a wet blanket in response to the last part of your comment, but it is known that there are infinitely many weird numbers, and 666 isn't one. But if there is a new odd weird number, that would be very big news indeed.
https://en.wikipedia.org/wiki/Weird_number

On 10/26/2024 at 3:14 PM, Satans Little Helper said: