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@@WrathofMath Wrath of Khan is referencing both the Movie and Khan academy. Really the academy reference is more important to me, but trekkies are, surprisingly, still a thing.
@@WrathofMath Early rap, btw, would be Public Enemy, Run DMC and The Beastie Boys. Later (much later cuz stepdads can be ashpits) I got into Snoop, Dre, Em and all that. Now it's MF Doom, Em, Dre, Snoop and Kendrick Lamar as far as lyricists, personally. And then it's Metro, Mustard, and a whole bunch of underground guys as far as that goes. Then a whole galaxy of other musicians from a wide range of genres. Also, I don't wanna leave out Yamé or Ren. 😎
It’s not that attempts *haven’t* been made to discover factors of double Mersennes up to MM(854933), or sieving for possible primes beyond there, but that those efforts have to date had no result - no factors have been found for MM(61) and higher.
@@Xanthe_Cat yea. i hope these new techniques and computer setups can manage to find the 5th double mersenne prime. imagine MM127 turns out to be prime. thats currently the only hope we have for a triple, quadruple, and quintuple mersenne prime.
The power of 2 in this Mersenne Prime has all digits from 1-9 except 5. But I am wondering if there is a Mersenne prime that has all digits 0-9? How many such primes are there if the digits can repeat more than once? What is the smallest Mersenne Prime that has all the 10 digits ?
Just the Mersenne numbers! They are easier to check, so those are the big record holders. There will inevitably be more primes found far less than this one that for now remain in the shadows.
All Mersenne primes are yet not tested above 2^57885161 - 1. Only 4 of those were found to be prime, including this new largest one. So there might be other Mersenne primes in between. In addition, there are all non Mersenne numbers that are too big to be tested. So, many other primes remain to be found ...
Yeah it has 41 million whatever digits, but that's in base ten. It's more natural to talk about how many binary digits a mersenne prime has. Especially when you realize the binary digits are ALL ones.
damn i wonder how many digits 2^9 - 1 is in binary (you'll never guess, but it's 9) Anyway, no, no it really isn't more natural. It might be more natural *for you*, but it isn't for most people.
I noticed that the title of this video doesn't include the word "largest". If we expand to all primes, not just the largest ones, then you've been discovering new primes every time you visit a web site.
They ran a program that tests whether for a particular prime p, the number 2^p-1 is prime. This is done using the Lucas-Lehmer test. The computer program they used is the result of almost 30 years of optimisation efforts.
I think I said something like "first failed candidate". There is some room for confusion here because there are "Mersenne primes" which are primes of the form 2^p - 1. Then there are 'Mersenne numbers', which are numbers of the form 2^n - 1. However in that definition, sometimes n is required to be prime, sometimes not, the definition is not universal. Regardless, 2^11 - 1 is the first number that is 1) one less than a prime power of 2 and 2) not prime. 2^4 - 1 is not prime, but it is also not one less than a prime power of 2, since 4 is not prime.
Aren’t new primes easy to find? It’s pretty easy to check if a number is probably prime (see Miller-Rabin primality test), and it works quickly even with monstrous 600-digit numbers, and we certainly haven’t found all of them.
@@davidespinosa1910Think of it as an expression, signalling that new discoveries can happen before big games come out of development. Don't get offended because a person uses such expression in their videos to convey a point across.
one of many non-serious math channels that have 90-video long series on Real Analysis and Linear Algebra and produce content for nearly a decade, yup 💀
