Is there any mathematical theory that treats prime numbers as the elements of some grander scheme? They certainly resemble the concept of chemistry elements on the periodic table.
In what way?
IANANTE (I am not a number theory expert), but as I understand it, the appeal of prime numbers is that no one has figured out the exact pattern at which they occur.
Things like the Riemann Hypothesis hold out the possibility that such a pattern or formula may be found.
This was all just fun and games until large, secretly-held prime numbers became the foundation of the RSA encryption algorithm. The aforesaid pattern also seems to bear some similarity to the allowed energy levels in quantum physics. (Now I’m REALLY out of my area of expertise).
So, in answer to the OP, yes, they seem to be part of a yet undiscovered scheme.
Are you thinking of the fundamental theorem of arithmetic? Unique factorization is a big deal, but the analogy between a list of primes and the periodic table is probably stretching it a bit.
hmm i seem to remmeber if you add two consecutive prime numbers and add or subtract 1 dont you always get a prime? if they number is greater then 5?
Tell me, are prime numbers a product of a base 10 counting system or do they exist in binary etc?
Base 10 is just a form of representation for a quantity. A given quantity is prime or composite regardless of its representation.
Nope, this is true for a fair amount of primes, but not as a rule. For example ,both 59 and 61 are primes, but neither 119 or 121 are prime.
Prime numbers do have a relationship to bases, though. You know that famously idiotic problem about 1/3? 1/3 is 0.333333. If you multiply 1/3 by 3, it gives you 1. But, if you multiply 0.333333 by 3, you get 0.9999999! Shocking! (Of course, the real answer is that 0.9999999 = 1).
This schtick will happen for more fractions than just 1/3. The same is true for 1/6 (0.16666 * 6 = 0.999999), 1/7 (0.14141414 * 7 = 0.999999), 1/9 (0.11111 * 9 = 0.99999) and many other numbers. In fact, the only fractions where that doesn’t happen are ones in which the denominator is formed with the prime factors of the base.
For instance, base 10 has the prime factors 1, 2, 5, and 10. So, 1/1, 1/2, 1/5, and 1/10 are all cool. So are any permutation of those factors - 1/4, 1/20, and 1/800 will all work. The only ones that won’t are ones which can’t be reduced to this set of prime factors - like 1/6, 1/7, 1/9, 1/11, or 1/600.
Interestingly, this holds true when you go into different bases, too. In base 7, 1/2 is all kinds of messed up, but 1/7 is fine. In base 2, no fractions are messed up.
I don’t know if any of this has any mathematical application or a name, really. It’s something I figured out in 8th grade while bored in Spanish class. I showed my math teacher, and she nodded kind of disinterestedly, but said all my work was right, at least.
One way: Lead cannot be turned into gold. 7 cannot be turned into 19.
Both are the basic building blocks of a certain level of organization.
from ultrafilter’s link: ‘Prime numbers are the basic building blocks of any positive integer, in the sense that each positive integer can be constructed from the product of primes with one unique construction.’ ex: 1200 = 2x2x2x2x3x5x5
Analogy: prime #'s like elements, non-primes like compounds
This looks likes the matrix code.
Can someone please explain to me why 2 is considered prime other than ‘it fits the formulas’? It’s driving me nuts because of course i can see it dividing up evenly in my mind.
If 2 isn’t prime, then you can’t express any even number as a product of primes. That’s would make the prime numbers rather useless as a concept.
:dubious:
A prime number is a natural number which has exactly two distinct natural number divisors, 1 and itself. The number 2 is a natural number (positive integer) and has exactly two divisors, 1 and 2. That’s why 2 is prime.
Cannot be turned into?
To comment on the OP, I don’t think the analogy between chemical elements and prime numbers is a very deep one. If we consider primes analogous to elements, and multiplying primes to get new numbers is analogous to combining elements to get new compounds then:
-I can multiply as many primes as I like, of whatever kind I like. Elements, however, have strict rules about what can be combined with what.
-Elements combine to form compounds which are often radically different from the constituent elements. Sodium is a metal that reacts explosively with water, chlorine is a poisonous gas. Combine them to get table salt. I can’t think of any similar emergent properties of non-prime numbers.
-There are an infinite number of primes. There is a finite number of elements.
I could go on, just considering the structure and behavior of atoms that has no analogy in prime numbers, but you get the point.
Okay. 2 and 5. My bad. It’s pretty much the same, right?
I knew I shouldn’t have posted that without looking into more than I did when I was 14. I’m a freakin’ idiot.
I think your proposition is correct, and it’s an interesting one: a rational number x will have a terminating n-ary expansion if and only if the denominator of its representation as an irreducible fraction has only as prime factors the prime factors of n. At first I only glanced at your post and wasn’t really sure what you were trying to say. I’d like to find a proof of this fact, though (not right now because I’m tired, but I’ll think about it tomorrow); or you can post yours if you want.
Now, one answer we could give to the OP is that in number theory, the fact that primes are the “building blocks” of (integer) numbers is very often used. For example, if you want to prove that a proposition is true for all integers n, you only have to prove that it is true for all primes, and that if k and l are integers, and the proposition is true for k and l, then it is true for kl. You can’t learn about number theory without seeing primes everywhere, even in places where you wouldn’t expect them. So they are truly the building blocks of our number system, in the same way elements are the building blocks of chemistry, but I wouldn’t try to go much further with this analogy.
Nothing to contribute except that I read elements as elephants. All the way through the first couple posts. 
This makes much more sense now.