Posted on 10/24/2024 12:36:35 PM PDT by Red Badger
It is the 52nd Mersenne prime to be found since they were first studied over 350 years ago.
A spiral representing primes.
Image credit: Bocskai Istvan/Shutterstock.com
The largest prime number ever discovered has been found by an amateur mathematician using Great Internet Mersenne Prime Search (GIMPS).
Prime numbers, as you likely learned in school, are numbers that can only be divided by one and themselves. There are an infinite number of them, with all numbers greater than 1 being either a prime number or a composite of primes. But having discovered a whole lot of them, new primes are now notoriously difficult to find.
Mathematicians are not totally ignorant of how to find them, nor forced to go through each individual number and check. Mersenne primes are an example of a prime with a nice pattern to them, as they can be expressed as 2P-1, or 2 to the power of a prime, minus 1. Small ones include 31 (25-1) and 127 (27-1), but they scale pretty quickly – and recent ones have generally been found with the help of computer power.
The Great Internet Mersenne Prime Search (GIMPS) looks for these Mersenne primes, allowing anyone to download software and help search for them, with a $3,000 reward for anyone who comes across one. The last 18 Mersenne primes have been found by GIMPS, and now 36-year-old researcher and former NVIDIA employee Luke Durant has found the largest Mersenne prime so far by developing infrastructure that can run GIMPS across many GPU servers.
Durant, from San Jose, California, found the prime number 2136,279,841-1, with the prime number taking the name M136279841.
"Physicists keep talking about, you know, information in the universe being an important first principle, so let me go try to find a new unique piece of big information and see if that helps guide my thinking about large numbers," Durant told Numberphile, explaining his motivation to try to find it.
"It was it was it actually pretty exciting to me to you know reach a scale of genuinely a global supercomputer put together in my office and [it] found a unique result. It's pretty fun," he added.
Proving numbers are prime gets really interesting. With smaller primes, say 11, it's an easy task. Simply divide it by all the smaller integers (1-10) and see if you are left with any integers. If it is only divisible by 1 and itself, it's a prime, as it can't be made from two smaller numbers. That's what a prime is. But for larger numbers, say 15,678,547,356,947 for example, you can see how it would be more time-consuming. Fortunately, mathematicians have some pretty neat tricks to test if a number is a prime or not, without resorting to working out if 15,678,547,356,947 is divisible by 3,187.
One method, described by Numberphile below, involves calling "witness" numbers to test if the number is prime. This gets complicated, with some numbers being better witnesses than others.
VIDEO AT LINK.....................
To test this prime number, GIMPS first performs a Fermat Primality Test, which can tell you whether the number is likely to be a prime. The new prime passed, but unfortunately, there are a small fraction of numbers known as "Carmichael numbers" which give false positives for prime numbers, meaning you can't be fully sure it is a prime using this method.
They then used the more definitive Lucas-Lehmer primality test for determining if Mersenne numbers are primes, finding again that the candidate is a prime. The team opted for October 12 as the date of discovery, the date that the Lucas-Lehmer test was run.
VIDEO AT LINK.....................
Credit for the discovery goes to Durant, Mihai Preda, and George Woltman for designing the software, and Aaron Blosser for maintaining the server. The new prime, as well as being the largest known prime number, adds to GIMPS' dominance in finding Mersenne primes, and becomes only the 52nd known Mersenne prime since they were first studied over 350 years ago.
PRIME PING!........................
What a breakthrough, now I can rest peacefully now.
Mathematical Ping!..............
But as one who also has a lifelong interest in "pure" mathematics, it's nice to know that there are still folks pursuing primes for their own sake (or to win a competition or prize). I mean, somebody's gotta do it, right? :-)
I would bet that the next prime number will be a prime number distant from this one, +/-1.............
Can’t read the article. Already have a headache just reading the Title.
For those who enjoy Math…rock on
Broken!
This is horrific news and has deleterious consequences for future uses of mathematics...
Thank goodness for million man march math as a work-around...
Some day they will get to the number that represents the entire universe :)
Hey that’s the number of my MasterCharge credit card! How did they steal it?
42
I don’t know. Did you ever happen to notice that 47 is a prime number.
I just blew my cerebral cortex reading this article.
Some day they will get to the number that represents the entire universe :)
And the stars will begin to wink out!
“And the stars will begin to wink out!”
“And you and I will simply fly away”.
You will have be a sharp music buff to get it.
Some genius physicists already think the total amount of energy in the universe ( positive energy of matter and negative energy of gravity) is zero....so that’s a good number to start at.
And…
2025 = 45 ^2 (45 to the 2nd power)
2024 = 44 * 46 (Obama * Biden)
The Math is with Trump ;-)
I submit Infinity devided by 2.
The only prime number I am interested in is the credit card prime number.
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