The largest Mersenne prime is 2^82589933-1....so far

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Breaking news! We found a new biggest Mersenne prime (and by extension, also the biggest prime we know): 2^(136, 279, 841)-1!

mkiiespi

Best Math professor on YouTube hands down.

Darkev

Update: A larger number has been found, which is: (2^(136, 279, 841)-1)

omargaber

could you make a playlist for the AXIOMS OF SET THEORY

khalilmohammed

The MERSENNE PRIMES formula is part of the following formula
1. Let a, b, n be natural numbers with a>b
- is always a natural number. If is prime then a-b is prime. If a-b is composite, then is composite.
- If [(a^n)-(b^n)]/(a-b) is prime, then n is prime. If n is composite then [(a^n)-(b^n)]/(a-b) is composite.
2. Let a, b, n be natural numbers where n is odd
- With a+b being odd, is always a natural number. If is prime then a+b is prime. If a+b is composite then is composite.
- If [(a^n)+(b^n)]/(a+b) is prime, then n is prime. If n is composite, then [(a^n)+(b^n)]/(a+b) is composite.

namduonghoang

I gather it would have been way too involved to go into in this video, but this begs the question, "How does the Lucas-Lehmer test work for Mersenne numbers?"
Anyone who's fiddled around with Mersenne candidates, M(p), where p is prime, has likely noticed that any prime divisors of M(p) are always of the form, 2kp + 1.
But the Lucas-Lehmer test is apparently more streamlined than that.

Fred

ffggddss

Is it possible there are prime numbers between any of the 7 largest prime numbers?

arnavbhavsar

I’m not sure why, but I started wondering if Rayo’s number could be prime. Then I started to wonder whether or not any properties of such a number could be known given the description of the actual number is too large to be written using the matter in the observable universe.

Then I wondered if the largest prime less than Rayo’s number might actually require more than a googol symbols to be described.

Finally, I’m wondering if there’s a way to place a civilization/entity on the Kardechev scale that could actually make practical use of Rayo’s number. I’m guessing it has to be higher than 7. Can such a thing even exist?

zemoxian

Hmm I'm probably being a dunce here but wouldn't it be easier to check for the factors of a candidate n -1 or n+1 and then use that information to check if n has any factors?

feynstein