German discovers longest prime number

[bemildred]

A German eye specialist with a keen amateur interest in mathematics has discovered the world's largest prime number after a 50-day search using his personal computer.

Dr Martin Nowak, who has his own practice in the south German town of Michelfeld, stumbled upon the number last week, breaking the previous record for a prime number by half a million digits.

Prime numbers are divisible only by themselves and 1. While the first prime numbers 2, 3, 5, and 7, are easy to identify, Dr Nowak's monster prime number is more than 7.8m digits long and is written as 2 to the 25,964,951st power minus 1.

The number belongs to a special class of rare prime numbers known as Mersenne primes, named after a 17th century French monk who first studied them 350 years ago. So far only 42 have been found.

Guardian UK

[underpants]

1. Good I was worried that that field of study was suffering

Glad to see someone is still working on it.

[beyurslf]

2. I have never understood how something can be the largest number.

Can't you just add a 0 or 5 or something and make it a little bigger? :)

[lazarus]

3. not and still be prime

For instance, 5 is a prime number. If you add one to it, it's no longer prime, it's 6. Add 2 to 5, and it's prime, but add 3, 4, or 5, and it's not.

Also, there's no known way to predict when a prime number will pop up.

[phantom power]

7. There is no largest prime.

One of the first theorems you learn in number theory.

Another example of sloppy science journalism!

[AZCat]

8. I was under the impression...

that there were a finite number of primes.

This would mean that there is actually a largest prime number.

[phantom power]

9. nope. there is an infinite number.

The proof is pretty simple, by contradiction:

Suppose the number of primes *was* finite. let the set {p1, p2, ... pN} be the set of all primes.

Now, define a value q = 1 + (p1 * p2 * ... * pN). Notice that "q" is not divisible by any of {p1, p2, ... pN}. But that makes it prime, since any non-prime number is the product of some set of primes.

Therefore, the set of primes cannot be finite.

[AZCat]

10. I was wrong, but there is a small error in your post

I read up on this, and while you are correct that there are an infinite number of primes, your conclusion is incorrect (I didn't think of it - Euclid did). It is possible that "q" is not prime, but rather is divisible by some prime not included in the finite set. The result is the same - the set does not include all known primes.

[phantom power]

12. right, that's part of the contradiction.

If the initial assumption (there's a finite number) were true, there can't be any other primes in the set, by definition.

[aden_nak]

4. There are forty-two of them? Adams was right. ^.^

[Oreo]

6. YES!

It took them this long to realize Adams wasn't kidding about 42.

[madhat]

5. The Jews had hidden it. n/t

[Igel]

11. GIMPS!!!!!

He was running GIMPS software. No line, no waiting ... download your copy now.

http://www.mersenne.org/prime.htm

(I would, but after a long run of Seti-at-home, I'm curring running Folding at Home in the background.)