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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."
GIMPS (Great Internet Mersenne Prime Search
They have Windows, Linux, FreeBSD, and OS/2 clients.
It is confirmed that it is a prime, but it hasn't yet been confirmed that it is the 42nd largest prime, because some numbers have not been checked.
From TFA:
However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M20,996,011 is actually the 40th Mersenne prime.
I'll probably be modded down for this...
GIMPS is the name of the project that apparently was responsible for finding this, so the parent was a joke, not flame bait.
The best reason for large Mersenne prime numbers that I can think of is that it gives data for mathematicians to formulate conjectures. There are many consequences to theoretical breakthroughs in the field of prime numbers, especially in the field of encryption, as the RSA algorithm requires large prime numbers.
Note: This new prime number by itself is USELESS for encryption. There are only 42 Mersenne numbers, so they can't be used because there are insufficiently many.
E = m c^3 Don't drink and derive E = m c^3
The top three previously known primes were Mersenne. Here's a list. At the time they were discovered, almost all largest Mersenne primes have held the record for biggest prime until being edged out by another Mersenne prime. I am not sure when a non-Mersenne last had that status, but it is a rare occurrence.
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Looking for Mersennes is "picking the low fruit" when it comes to prime hunting so I question the phrasing "Not only is it the biggest Mersenne
What would have been remarkable would have been if the new largest prime were *not* a Mersenne.
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
actually its 25964951 :)
You mean a number which is the *sum* of all of its divisors except itself.
A number which is the product of all its divisors except itself is, well, any product of exactly two primes.
Just started my PC to compute it:
echo "2^25964951-1"|bc -l>prime
If you put 'time' in front, the system will tell you how long it takes.
Just checked that 2^1000000 took about 8,5s, but it is not linear. I expect it to take some 15 minutes one my AMD64
That is not true. The number p1*p2*....*pn+1 is either a prime, OR it has a factor that is not one of the p's. In either case, you have a new prime, which as an aside proves that there are infinitely many primes.
E = m c^3 Don't drink and derive E = m c^3
is the Mersenne Twister (MT), a pseudorandom number generator.
Pseudorandom number generators are periodic, that is they start repeating the sequence of "random" numbers, after a while. This is bad. The period of the MT is as big as the Mersenne Prime that you choose to base the algorithm on. So, if you wanted a REALLY long period, you could use this new prime. In practice, however, very few people need this long of a period.