Thread: why are primes called the building blocks of numbers?

2 3 5 7 11 etc
what makes them the building blocks of numbers?

I do not know why "primes" are considered the root of all numbers or where it is that you have been suggested that they are the root of all numbers. In your list you truncated the list by beginning it with 2. The first prime number is 1. 0 is not considered a prime number since it is divisible by any number except itself. The definition of a prime number is a number that is divisible only by itself and 1 without leaving a remainder. It has been a while since I have considered primes and that being said I do not know what the largest known prime number known to man is or if an algorithm has been discovered that can be used to be a prime number generator other than brute force (i.e. a formula relatively easily implemented by man instead of very redundant number crunching). In my opinion irrational numbers can also be considered roots of all numbers since they include numbers such as pi and e which are infinitely indivisible (i.e. they go on and on and on). Those two irrational numbers are demonstrated over and over again in our physical world (i.e. volumes,areas, and distances and radioactive decay, etc.) and since math is a way to describe our physical world does it not seem more appropriate to consider those two numbers, irrational though they may be, as the root of all numbers.

Because every integer can be written as the product of primes together with a unit (). The remarkable fact is that this product is unique, if one ignores the order in which the factors are written. That is, for each such product, there is one and only one integer. Likewise, for each integer, there is one and only one such product.

This is called the Fundamental Theorem of Arithmetic, and, although easy to see using fingers and toes, is strangely hard to prove rigorously.

Originally Posted by Guitarist

Because every integer can be written as the product of primes together with a unit (). The remarkable fact is that this product is unique, if one ignores the order in which the factors are written. That is, for each such product, there is one and only one integer. Likewise, for each integer, there is one and only one such product.

This is called the Fundamental Theorem of Arithmetic, and, although easy to see using fingers and toes, is strangely hard to prove rigorously.

i remember that from 6th grade. we probably didnt go into details but we used it when writing factor trees, or probability. i forgot though.

but thank you for reminding me of that theorem.

Originally Posted by wojowhiskey

The first prime number is 1.

1 isn't considered i read. one is used in defining primes so i guess it's not really part of it i'm guessing.

Prime numbers are very interesting to mathematicians.

The Answer: Prime Factorization
You can read down to "Why?"

Also, for fun, look at this:
Ulam spiral - Wikipedia, the free encyclopedia

Now that the thread has been answered, I'll just make an observation.

What I find interesting as a perspective math teacher is how much time we spend on things like teaching prime numbers when we also know it's of almost no practical use for the vast majority of people who actually use mathematics--like engineers, bankers, logisticians and scientist.

The process is called getting an education. It's OK to be guided by "practical use" but one shouldn't be guided by it exclusively. There are many instances in the history of mathematics where the practical use of new findings was not immediately apparent.

The process is called getting an education.

Sounds a lot like an appeal to tradition. But I'll frame a suitable thread starter in the education sub-forum.

Well, I agree that it could, in a more general sense, be more of an educational topic. But here it's associated with mathematics. And it's really just the simple note that advances in mathematics should not be relegated to those pursuits considered to be of practical use. Certainly, I think, that such an argument (pursue the practical) may have more validity with respect to other subject matter than mathematics.

Certainly, I think, that such an argument (pursue the practical) may have more validity with respect to other subject matter than mathematics.

My simple point is the vast majority of mathematics, even of the highest power, is of the practical kind. Almost all the ways mathematics get used today demand it's practitioners have great skill at thinking mathematically to figure out the problem, information needed and what process should be applied, programing and than interpreting that information while letting computers do the calculating. Yet we still put all all our educational effort on teaching calculating just as teachers did five decades ago, before we had computers. I've done computer modeling of clouds, army supply and transportation models, disease spread models, been a weapons testing officer and served as an analyst--all using lots of mathematics. BUT, in those several decades you know what I've never had to do? Solve a quadratic equation by hand, or do anything which required an explicit knowledge of prime numbers, or what trick I had to apply to solve a calculus or partial differential equation. What had to know is how to analyze a problem mathematically and apply it through programing into functions to get a result I needed--and then how to examine the output so it was meaningful. Kids need practical math knowledge they'll remember like evaluated loan repayment options, life insurance or knowing when a statistically report cited on MSNBC is bullshit. Even if they go onto engineering or science, their ability to do complex math will have little to do with their ability to crunch calculations. Our math standards are half a century obsolete dating back to when a "calculator" was a job profession instead of a machine.

Don't hold back. Tell us how you really feel! Lol!

What you are advocating is actually a really old argument. And not without merit. I was doing algebra homework in 8th grade and after my father looked at it he said what you said, basically. Of course his words were different but the point was the same.

I'm not sure how to measure it but I suspect that the vast majority of mathematics is not of the practical kind.

Personally, I enjoy studying mathematics for its intrinsic value. I too have seen very little need for much beyond arithmetic and basic algebraic principles except perhaps to explain certain things in the real world that math can model.

But, I still feel that just pursuing the practical would be a bit dull, I guess.

Originally Posted by brody

2 3 5 7 11 etc
what makes them the building blocks of numbers?

Prime numbers are really backbone of numbers as you know there are various numbers in Prime Numbers list which is quite useful . So we must agree with it .