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42nd Mersenne Prime Confirmed
Jazzer_Techie writes "The possible Mersenne Prime discovered last week has now been confirmed. This prime has 7,816,230 digits, which makes it not only the largest Mersenne Prime, but also the largest prime of any kind ever discovered. For those who don't want to take time to read the article, the prime is 2^25,964,951 - 1."
Can anyone post those digits in case the site gets /.'ed?
Those math freaks sure are a bunch of GIMPS.
This is the 42nd one? I wonder if that means anything...
Behold, another webcomic!
GIMPS (Great Internet Mersenne Prime Search
They have Windows, Linux, FreeBSD, and OS/2 clients.
yes. There is a theorem due to Euclid that every even perfect number (a number which is the product of all of its divisors except itself) is of the form
(2^n-1)*2^n. The given form does not apply to odd perfect numbers, but it is unknown whether any odd perfect numbers exist.
E = m c^3 Don't drink and derive E = m c^3
I found it by leaving my browser open for a while on this page.
There actually are very good algorithms for finding primality. It has reached the point where proving a number prime is MUCH easier than finding any factors of it.
There are two types. One is deterministic, and will give you absolute proof that the tested number is prime. The other type is probability based. These are more popular. The most widely used is known as the Miller-Rabin test. It is known to be absolutely correct for all n 3*10^16. For larger n, it will never report a composite to be prime, but there is a small (around 10^-20) chance the "prime" number will be composite. There are no known prime numbers that Miller-Rabin reports to be composite.
In the case of Mersenne numbers, it's a different story. There is a deterministic algorithm called the Lucas-Lehmer test. This will determine whether 2^p-1 is prime with O-notation p! The catch of course is that it only works for Mersenne numbers.
E = m c^3 Don't drink and derive E = m c^3