Speaking as a math-averse school teacher, I'm glad the game provides a way in for people with so many different learning styles. It will keep the playing community diverse.
Prime numbers: Any integer only evenly divisible by two other numbers - one and the number itself. It's that "by two numbers" that eliminates one out of the list.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53... That's all I can pull off the top of my head.
Yeah sure, god I wish I knew what language your speaking in duh - one and the number itself... This is as bad as algebra's stating you can tell if someone is lying....
There's that book "The Man Who Mistook His Wife for a Hat" in which Oliver Sacks describes twins who love to list prime numbers. Some people love the feel of math... Prime numbers somehow fit into the rhythm and structure of math. Some people just enjoy that.
@xoxJulie - Maybe if I use examples. Integers are the counting numbers (mostly): 1,2,3
There is no decimals or fractions involved. It also includes zero and negative numbers: 0,-1,-2,-3 Any whole number in fact.
So when I say any integer that can be divided by only two numbers, one and itself, I mean something like 3 is only divisible by 3 or 1 without leaving a remainder. Same as 2, 5, 7,11..
4 can be divided 1, 2, and 4... 3 numbers. 1 can be divided by 1 but nothing else divides into it so only one number. 12 can be divided by 1,2,3,4,6, & 12 - 6 numbers, and so on. How would you state what a prime number is? In general terms, without having to give many, many examples of what is and is not a prime number? I actually spelled out the number 1 in my previous definition just because that's a recommended practice in writing numbers in general for, well, stories, articles, and such. So when when I said "Any integer only evenly divisible by two other numbers - one and the number itself," you can break it down like this:
Any integer - pick any whole number.
Ok. Simple rule, other than zero, all numbers can be divided by 1. And any number can divided by itself (except zero since you can't divide by it).
Now, you have some number you picked, try dividing it by the numbers between it and 1. If any of those numbers can divide into the number you originally picked, then the number you picked is not a prime number. If you run through all those numbers and none divide into that originally picked number, then it is prime.
The idea of a prime number is the same idea of elements in chemistry. In chemistry every chemical is made up of simpler chemicals. And the simplest chemicals are the elements - and they aren't made up of anything else unless you start knocking about with nuclear physics. :) Hydrogen, Helium, Lithium, Carbon, Oxygen, Nitrogen, Argon, Iron, Gold, Silver, Tungsten (most metals are elements). So too with numbers. Every whole number is made up of prime numbers. "prime" simply means the basic, or fundamental numbers. As one person made an example of, they are used cryptography for one thing, but they show up elsewhere in mathematics, computer science, and other professions. Just like in chemistry, knowing the fundamental building blocks of anything is enabling. Once you know the properties of those building blocks and how they relate to other ones, you know what you can build and the best way to do it. :)
2 is the only even prime number, all the rest are odd.
And they are quite handy when you are trying to determine the least common denominator in fractions too... ;)
@Linnaea - super neat catch...did they change it for you? I may have to go rooting around for it if they haven't...but I hope they have...I think it's hilarious that the achievements are based on prime numbers.
One of my favorite books is by Peter Plichta where he describes his find of a Prime Number Cross in 1993...fascinating read quite frankly...
And yes, I'm a math g33k if you couldn't figure it out yet...
Thanks for the suggestion...I found the Art of Computer Programming, but not the Art of Mathematics...however Dr. Knuth's books look fascinating (and he seems like a hoot)...thanks for the great tip!
I thought it was Knuth, but I may have misremembered. I'll try to find it for you. And the "Art of Computer Programming" is considered a bit of a bible for programmers. I used to own several volumes. I hated to lose them. :(
I understand chemistry and the idea of elements being the lowest material and building from there yet the connection of math to a cooking achievement I can't even fathom. Unless we are talking about how many 1 egg, 3 meats etc. If that is the case, just the number regardless of what item it would seem a telephone book would drive a math geek nuts. I must be missing something here and am having a really hard time figuring out the what that's missing. But I am actually trying
Julie, I think what is being referred to is the achievement badges - for a lot of them, their achievement number is a prime number. At face value, they just look like a weird choice for achievement level, but they are primes. However, there are also those that are non prime (composite), so I assume that this is just for variety and for us to discuss in this thread lol!
Math and spelling were always good subjects for me :) History is the worst. I cannot understand how something done a million years before I was born in a primitive society by people whose names I can't pronounce, has any relative bearing on today. It's been explained to me a ton of times so don't bother trying because I still won't understand.
Julie-yes it is just a number of items needed to achieve a certain badge such as 13 friends to be splanked :)
Thanks Joby, thank god one less thing to think about for prime numbers. The only thing I could think of what I would use a prime number for is a birthday. Nice to know if it was going to be a prime year or not. Looking at the prime numbers listed above there are about 16 to 17 in 50 numbers so guessing there would be around 33 in a hundred, or 1/3 of all numbers are prime. Right?
Gee that's a big difference the first 100 numbers being almost/about 1/3 and the next 900 down to 168 or around 1/2 the amount of the first 100. Seems like a disparity, or harder to divide bigger numbers comes into play. Awck my brian just blew a fuse, needs soothing orb. I know later this week. lol
A simple theory holds that if you take a prime number and multiply it by two, there is at least one other prime number between the two values. Seems to work for me. :)
Leibniz determined that primes larger than 3 always occurred as multiples of the number 6 with the addition of 1 or 5 (ie, 6n+1 or 6n+5 for n=1,2,3,4,...)
Plichta refined the formula slightly and determined that for primes larger than 3, they are a subset of the set of numbers calculated by the formula 6n +/- 1 for n=1,2,3,4,.... [however, note that not all numbers derived by that formula are primes].