GIMPS is reporting that on 23 August a new Mersenne prime was reported to their server. Verification began today and should take about two weeks to complete. No word on what the prime was, how many digits, etc.

The last Mersenne prime discovered was , back in 2006 (blogged about here) and weighed in at a whopping 9,808,358 digits. Any bets on how big this new one is, if it’s really a prime? I’m guessing 10.5 million digits. Sounds like a good occasion for a nerd office pool.

**Update**: Isabel at God Plays Dice likes 14.5 million digits instead, and she’s actually using math and stuff to make that estimate instead of just shooting totally in the dark like I am.

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I started reading about Mersenne Primes on Wiki and all of a sudden started missing math, and school, and MOPS… Yikes!

If only I could go to school and get paid for it… that would be a great job!

You can! It’s called “graduate school”.🙂

Robert,

I’m an elementary teacher (aka Eileen) and have a question for you. Can you answer this for me simply, as I could explain to my eight-year-olds? I can explain what makes a number a prime number, but I cannot understand myself yet WHY certain numbers ARE prime. It would seem that prime numbers continue into infinity. I would like to understand the ESSENCE of what prime numbers really ARE. It seems normal to have small prime numbers, like 2, 3, 5, 7, 11, or 13. But getting into larger primes, I just feel like how is it that numbers can exist so large with no additional factors, other than that there must be a special MEANING that prime numbers describe. What is this MEANING? Or is this still something that mathemeticians themselves still wonder about but do not yet understand?

Best regards,

Madame Monet (aka Eileen, Dedicated Elementary Teacher)

@wpm1955: That sounds like a great excuse for another blog post, but let me sketch out an answer here.

First of all, yes, there are infinitely many primes. Euclid proved that in the

Elementsabout 2500-3000 years ago!As to what a prime number really

is, one explanation is that prime numbers are the “building blocks” of all integers in the sense that every integer can be factored into a product of them in an essentially unique way. (That’s the Fundamental Theorem of Arithmetic.) Prime numbers are to integers and arithmetic what atoms are to substances and chemistry.What does it mean that there will always be greater and greater prime numbers? That’s more of a philosophy question, I guess — maybe I’ll let others take a crack at that before I try.

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Robert,

I LOVE this explanation! It will be very easy now for me to explain to my third graders, by just asking them, “What are numbers made out of?” Then I can explain that numbers have building blocks (primes) just as words have building blocks (letters). Wow, this helps me, and will help them, too! Thanks!!!

Eileen

Actually, in third grade we do also already discuss how atoms are building blocks of elements, so this idea of primes being building blocks is very easy to understand.

This is an example of how basic conceptual ideas are often missing in elementary education in math. I didn’t know that primes were building blocks, and I am 53.

Eileen