Largest Prime Number to Date Discovered

AlphaAtlas

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Last month, Mersenne Research announced the discovery of the largest known prime number to date. Both the announcement and WolframAlpha say that 2 ^ 82,589,933 - 1 has nearly 25 million digits in base 10, which is apparently over one and a half million digits larger than the previous record holder, and the announcement also mentions that this is the 51st known Mersenne Prime. Using the same software that's frequently used to stress-test CPUs, M82589933 was reportedly discovered by by Patrick Laroche on December 7, 2018, and verified by others shortly afterward.

The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using three different programs on three different hardware configurations. Andreas Hoglund verified the prime using CUDALucas running on a NVidia V100 GPU in 21 hours. Andreas Hoglund also verified the prime using Mlucas running on 16 cores of an Amazon AWS instance in 72 hours. Aaron Blosser also verified it using Prime95 on an Intel 7700K processor in 6 days, 8 hours.
 

Grahamkracka

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For a mathematical layman, can someone explain the benefit of finding ever larger instances of prime numbers?

There isn't really. Large primes are used for encryption but numbers this large are useless there (for now, at least). In reality much of the search is just math for math's sake. A lot of basic research is like that, to answer questions nobody else has or currently cares about. Some becomes useful, some not so much....but we would never know if the questions weren't asked.
 

Criticalhitkoala

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For a mathematical layman, can someone explain the benefit of finding ever larger instances of prime numbers?

Since westward expansion is long gone, the only frontier left is either shitty (underwater), digital (primes, and other things), or not happening in our life time (instellar). I think things like these help fill that discovery void that is become more and more scarce.
 

Jagger100

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i thought they needed super computers for this
You need that to brute force it and never miss one. IF you use some tricks you can cut down the number of iterations to get a big one. There are likely Primes between this number and the last biggest number which may be unknown.
 

Joust

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As an alternative, may I humbly submit from the files of GenMay:
3z6tbtwum4821-png.132489
 

Grahamkracka

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You need that to brute force it and never miss one. IF you use some tricks you can cut down the number of iterations to get a big one. There are likely Primes between this number and the last biggest number which may be unknown.
There are likely millions of primes between this one and the previous largest number...There's a decent chance we'll never find one.
 

BloodyIron

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How exactly do you store a number that large from a computational perspective? Like seriously, 256-bit CPUs I don't think come even close to that, and we're operating on 64-bit CPUs.

o_O?!
 

SvenBent

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For a mathematical layman, can someone explain the benefit of finding ever larger instances of prime numbers?
prime numbers are needed for strong encryption as you need a lot of mod instruction
If you are not using a prime that means there are multiple correct solutions aka weakining the encryption.

But edge of science and math are not always about having a reason. most of the time we discover the a usage for it after we have determine the base knowledge.
 

chargin

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For those that didnt realise, like me, a Mersenne Prime is a subset of all primes. But this one is the biggest prime ever found. I think Mersenne Prime's are easier to find than a normal prime as you kind of have "a place to look" for them.


Mersenne Prime
a number of the form 2^p −1, where p is a prime number. Such a number which is itself prime is also called a Mersenne prime.​
 
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