Mathematician Claims Proof of Connection between Prime Numbers

[EncryptedBytes]

(http://news.yahoo.com/mathematician-...131737044.html)

A Japanese mathematician claims to have the proof for the ABC conjecture, a statement about the relationship between prime numbers that has been called the most important unsolved problem in number theory.

If Shinichi Mochizuki's 500-page proof stands up to scrutiny, mathematicians say it will represent one of the most astounding achievements of mathematics of the twenty-first century. The proof will also have ramifications all over mathematics, and even in the real-world field of data encryption.

Hmm. Am I reading this wrong, or (if true) could it be used to calculate arbitrarily large prime numbers?

[safeguy]

I have another theory.

Safeguy Prime Theorem:

Prime numbers are integers greater than 1, ending with the odd digits (1, 3, 5. 7, 9) AND is not divisible by 3, 5 and 7.

I haven't been able to prove it right but no one else I posed this theory to has been able to prove it wrong either.

[Hungry Man]

It's not about defining a prime number (we have a definition, always have) it's about coming up with a proof that shows a relationship. That means you can predict them/ calculate them, something we haven't been able to do.

Right now it's "is X a prime? Is X+1 a prime?", if this proof is correct it will be "if X is a prime then Y should be a prime too."

[MikeBCda]

Originally Posted by safeguy

Prime numbers are integers greater than 1, ending with the odd digits (1, 3, 5. 7, 9) AND is not divisible by 3, 5 and 7.

3,5,7 leaves the door wide open for errors. By definition, a prime number is an integer which cannot be evenly divided by any number other than itself (or 1, of course).

There have been algorithms proposed which work well up to a point in calculating primes, but so far every one has failed once you get to large enough numbers.

It'll be interesting to see how this new theory (I haven't yet read the news article) stands up to close scrutiny. My personal hunch is that it too will turn out to have an "upper limit" beyond which it fails.

[kupo]

Originally Posted by safeguy

I have another theory.

Safeguy Prime Theorem:

Prime numbers are integers greater than 1, ending with the odd digits (1, 3, 5. 7, 9) AND is not divisible by 3, 5 and 7.

I haven't been able to prove it right but no one else I posed this theory to has been able to prove it wrong either.

1. Get two random prime numbers (except 3,5,7). E.g. 13 and 17.
2. Multiply the two random prime number. 13*17 = 221.
3. 221 is greater than 1.
4. 221 is an odd number.
5. 221 is not divisible by 3, 5 and 7.
6. 221 is NOT a prime number.
Safeguy Prime Theorem is proved to be wrong. Do I get a price?

[MikeBCda]

Oh, forgot one other goof, that "greater than 1" thing. IIRC, 1 itself is considered a prime. Can't remember about zero, think there's differences of opinion about that one -- or maybe I'm thinking of Fibonacci (sp?) numbers, of which zero is usually considered the first.

[Thankful]

Originally Posted by MikeBCda

Oh, forgot one other goof, that "greater than 1" thing. IIRC, 1 itself is considered a prime. Can't remember about zero, think there's differences of opinion about that one -- or maybe I'm thinking of Fibonacci (sp?) numbers, of which zero is usually considered the first.

The first prime number is 2.

[safeguy]

Originally Posted by skudo12

1. Get two random prime numbers (except 3,5,7). E.g. 13 and 17.
2. Multiply the two random prime number. 13*17 = 221.
3. 221 is greater than 1.
4. 221 is an odd number.
5. 221 is not divisible by 3, 5 and 7.
6. 221 is NOT a prime number.
Safeguy Prime Theorem is proved to be wrong. Do I get a price?

Nice. Your post gave me an idea...so I come up with another theorem. I know it's cheating but it's all for a good cause

Safeguy Revised Prime Theorem:

Prime numbers are integers greater than 1, ending with the odd digits (1, 3, 5. 7, 9) AND is not divisible by integers greater than 1, also ending with these odd digits.

[FanJ]

Originally Posted by Hungry Man

-snip-

Right now it's "is X a prime? Is X+1 a prime?",

-snip-

If X is a prime AND if X>2, then X+1 is not a prime.
Reason: X+1 is divisible by 2.

[FanJ]

Fermat:
Consider the equation a**n + b**n = c**n
(I don't know whether the board software allows better representation for a**n)
With a, b, c and n being natural numbers AND n>2 there is NO solution.
With n=2 there are well known solutions such as a=3, b=4, c=5.
3**2 + 4**2 = 5**2
9+16=25

http://en.wikipedia.org/wiki/Prime

http://en.wikipedia.org/wiki/Fermat%27s_last_theorem

[myrti]

Originally Posted by safeguy

Nice. Your post gave me an idea...so I come up with another theorem. I know it's cheating but it's all for a good cause

Safeguy Revised Prime Theorem:

Prime numbers are integers greater than 1, ending with the odd digits (1, 3, 5. 7, 9) AND is not divisible by integers greater than 1, also ending with these odd digits.

Wrong again. :p 3 is a prime. It's greater than 1, it ends in odd digits (3), and it is divisble by 3 (so an integer greater than 1, ending in this odd digit). Hence your theory does not correctly define prime number. Also 2 is a prime and does not end in odd digits.
So both the condition ending in odd digits and "not divisible by integers greater than one ending in odd digits" can be falsified by prime number.

This being said " a prime number is a number that can only be divided by itself and 1" is the definition not a theorem. This is essentially what you're theory now says, except that you've removed all the multiples of 2 by only looking at odd numbers.

regards myrti

[FanJ]

Originally Posted by myrti

-snip-

This being said " a prime number is a number that can only be divided by itself and 1" is the definition not a theorem.
-snip-

A prime number is a natural number greater than 1 that can only be divided by itself and 1.

[DBone]

I'm going to have to wait for the movie

[Hungry Man]

Defining a prime number is completely irrelevant. We already have a definition. What the proof is about is the relationship between primes, which can be used to find new primes.

All a definition does is show us what a prime is, not how to find it.

[FanJ]

Originally Posted by Hungry Man

Defining a prime number is completely irrelevant. We already have a definition. What the proof is about is the relationship between primes, which can be used to find new primes.

All a definition does is show us what a prime is, not how to find it.

Of course we have already a definition about what a prime number is. Without definitions (and axioma) mathematics is nowhere. There is just too much confusion in this thread about mathematics and the definition of a prime number in particular.

[myrti]

Originally Posted by FanJ

A prime number is a natural number greater than 1 that can only be divided by itself and 1.

Yes. My bad.

[MikeBCda]

I was interested enough to take a look over at Wikipedia hoping to find an explanation of why 1 isn't considered a prime number. Apparently it has to do with the process of finding the prime-number factors that make up a non-prime, and specifically breaking them down into their "primest" form.

As an example, 21 can be expressed as 7x3 or as 7x3x1. For reasons I didn't understand, this apparently screws up determining the simplest factors, so 1 was excluded from the definition of primes to eliminate this mysterious (to me) problem.

While off topic, the brief side-trip into Fermat's last theorem was interesting, and ranks up there close to the meaning of life. It's well known that x^n + y^n = z^n (someone here was asking about alternative notation for powers, and that's the one I learned in school) has many possible solutions for x, y and z where n=2 (the Pythagorean relation in geometry is probably the best-known example). But so far no one's been able to come up with a proof, for or against, for the existence of any solution where n>2.

(Edit) My bad ... according to the Wikipedia article, this was finally proved back in 1995. Odd I missed that, since (a) math has always been one of my favorite subjects, and (b) it would have to have been major news.

[FanJ]

Originally Posted by FanJ

Fermat:
Consider the equation a**n + b**n = c**n
(I don't know whether the board software allows better representation for a**n)
With a, b, c and n being natural numbers AND n>2 there is NO solution.
With n=2 there are well known solutions such as a=3, b=4, c=5.
3**2 + 4**2 = 5**2
9+16=25

http://en.wikipedia.org/wiki/Prime

http://en.wikipedia.org/wiki/Fermat%27s_last_theorem

I have been wondering who actually would find me not being precise enough there. I should have said:
With a, b, c and n being positive natural numbers AND n>2 there is NO solution.