UCLA's 13 million-digit prime number could win $100,000


LOS ANGELES (AP) -- Mathematicians at UCLA have discovered a 13 million-digit prime number, a long-sought milestone that makes them eligible for a $100,000 prize.

The group found the 46th known Mersenne prime last month on a network of 75 computers running Windows XP. The number was verified by a different computer system running a different algorithm.

"We're delighted," said UCLA's Edson Smith, the leader of the effort. "Now we're looking for the next one, despite the odds."

It's the eighth Mersenne prime discovered at UCLA.

Primes are numbers like three, seven and 11 that are divisible by only two whole positive numbers: themselves and one.

Mersenne primes -- named for their discoverer, 17th-century French mathematician Marin Mersenne -- are expressed as 2P-1, or two to the power of "P" minus one. P is itself a prime number. For the new prime, P is 43,112,609.

Thousands of people around the world have been participating in the Great Internet Mersenne Prime Search, a cooperative system in which underused computing power is harnessed to perform the calculations needed to find and verify Mersenne primes.

The $100,000 prize is being offered by the Electronic Frontier Foundation for finding the first Mersenne prime with more than 10 million digits. The foundation supports individual rights on the Internet and set up the prime number prize to promote cooperative computing using the Web.

The prize could be awarded when the new prime is published, probably next year.

This is good stuff.

By the way, there is a lot which is not known about Mersenne primes.

There are infinitely many prime numbers. But not every prime number is Mersenne.

It is unknown whether there is a largest Mersenne prime.

It is completely possible that the number discovered by these researchers is the largest and final Mersenne prime ... meaning that there are no others to be discovered.

What's cool about Mersenne primes is that even though they are extremely scarce they grow exponentially ... and so whenever (on the rare occasions that) a new Mersenne prime is found ... it also becomes the largest known prime number.

quote:

Originally posted by HonestBrother:
... and so whenever (on the rare occasions that) a new Mersenne prime is found ...

I was wondering if this would be interesting or to you mathematicians! Of course I have no understanding of what all the hoopla is about!

And although you kinda answered my question above ... just how rare is it to find one of these number??

When should we expect the next one to surface?

quote:

Originally posted by EbonyRose:

quote:

Originally posted by HonestBrother:
... and so whenever (on the rare occasions that) a new Mersenne prime is found ...

I was wondering if this would be interesting or to you mathematicians! Of course I have no understanding of what all the hoopla is about!

And although you kinda answered my question above ... just how rare is it to find one of these number??

There are only 46 of them ... and the latest one has 13 million digits.

Can you imagine that?

If you look among all the numbers that have 13 million (or fewer) decimal digits ... there are only 46 of these things.

That's pretty rare.

To give you some idea:

There are only 3 Mersenne primes less than 1 hundred:

3, 7, 31

There are only 4 Mersenne primes less than 1 thousand:

3, 7, 31, 127

There are only 7 Mersenne primes less than 1 million:

3, 7, 31, 127, 8191, 131071, 524287

ETC.

quote:

When should we expect the next one to surface?

If we're lucky? Computer power being what it is ... Maybe within the next 5-10 years.

This message has been edited. Last edited by: HonestBrother,

I'M AN ELITIST TOO.

Hmmm .... 13 million digits, huh ...

How many commas is that??

quote:

Originally posted by EbonyRose:
Hmmm .... 13 million digits, huh ...

How many commas is that??

That would be nearly 4 and a half million commas.

4,333,333 of them to be precise.

Get the hell outta here!!!



And now what, exactly, would I do with a number like that??

I would use it to ....

Hey HB ...

Perhaps you thought I was joking, but ... I meant that to be a serious question!

The prime number (in and of itself) does what, exactly??

and

Can anything really be done with a number that big? Or is it a more symbolic - and the excitement is more centered around the fact that a number that large can be found??

And lastly ... could a human being, without the aid of a computer, ever have discovered that number?

quote:

Originally posted by EbonyRose:

The prime number (in and of itself) does what, exactly??

Prime numbers are (in a sense) the building blocks of the integers.

I'm not sure I can give you a convincing reason why you personally should be excited about them. But there are people who study prime number theory like other people study the stars. They get excited about these obscure objects that most people could care less about.

quote:

Can anything really be done with a number that big? Or is it a more symbolic - and the excitement is more centered around the fact that a number that large can be found??

There are a number of reasons (both theoretical and practical) why one might be excited about such a discovery.

On the theoretical side, there are a number of unanswered questions about mersenne numbers. There is for example the quantitative question of exactly how many of them are prime. It is possibly the case (but completely unknown whether) they are infinite in number ... and then there are qualitative questions surrounding their distribution.

One practical reason they are of interest is that they do sometimes produce large primes ... which are of interest in cryptography.

quote:

And lastly ... could a human being, without the aid of a computer, ever have discovered that number?

Oh sure ... If the human being had a couple of hundred years to live. The computers are programmed with algorithms that (in theory) could be performed by a human being. But the time involved in doing so is ridiculous.

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quote:

Originally posted by HonestBrother:

quote:

Originally posted by EbonyRose:

The prime number (in and of itself) does what, exactly??

Prime numbers are (in a sense) the building blocks of the integers.

Okay .. and an "integer" (in plain English) is ...

I looked it up and the definition left me even more confused.

"A complete entity" would be like a whole number? Or a number that somehow sustains itself??

And this "prime number" (the normal ones) does what, exactly??

My nephew now has a 14 y/o step-son and when I'm over there sometimes and homework time (interestingly enough) the men (my brother and/or both nephews) jump in to help him with it and are talking about these things that you're saying .. and, I have NO clue!! And I mean none.

However, they did a "square root" explanation for him a while back .. and some things came back (from the lifetime-ago math classes I had to take to get from school) .. and, it was all really kind of interesting!

So ... that's why I'm asking ... because, at least at the moment,0 there is something in the way of 'interest' forming in my brain ... and while I have access to a mathematician ... I might as well make use of you!

So I'll in advance for your patience and attention.

quote:

Originally posted by EbonyRose:

quote:

Originally posted by HonestBrother:

quote:

Originally posted by EbonyRose:

The prime number (in and of itself) does what, exactly??

Prime numbers are (in a sense) the building blocks of the integers.

Okay .. and an "integer" (in plain English) is ...

I looked it up and the definition left me even more confused.

"A complete entity" would be like a whole number? Or a number that somehow sustains itself??

The integers include the whole numbers.

Integers are numbers like: ...., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...

Basically the whole (or counting) numbers, plus zero, plus the negatives of the counting numbers.

quote:

And this "prime number" (the normal ones) does what, exactly??

Every integer can be completely factored into more basic parts:

2

3

4 = 2 x 2

5

6 = 2 x 3

7

8 = 2 x 2 x 2

9 = 3 x 3

10 = 2 x 5

11

12 = 2 x 2 x 3

13

14 = 2 x 7

15 = 3 x 5

ETC.

The more basic whole numbers are called prime numbers (2, 3, 5, 7, 11, 13, etc.)

This is the sense in which the prime numbers are the building blocks.

Did that make sense?

quote:

Originally posted by HonestBrother:

Did that make sense?

Absolutely!!! Very much so!


AND .. it didn't hurt one bit!!