A Law of Primes

[the tree]

Okay I have to ask, where on earth did you make the leap between "not divisible by 3" and "probably a prime"?

 

If we pick a couple of numbers, we can run them through any amount of divisibility tests.

 

Try 1921 and 2311 for utterly contrived examples.

 

• The last digit in both cases is odd.
  They've failed the divisibility test for 2 - does that make them both prime?
  
• The sum of all digits in both cases is not divisible by 3.
  They've failed the (your?) divisibility test for 3 - does that make them both prime?
  
• The last digit in both cases is not 0 or 5.
  They've failed the divisibility test for 5 - does that make them both prime?
  
• The last digit, subtracted from the rest of the number, is not divisible by 7 in either case.
  They've failed the divisibility test for 7 - does that make them both prime?
  
• The sum of every second digit minus the sum of the remaining digits, is not divisible by 11.
  They've failed the divisibility test for 11 - does that make them both prime?

 

As it happens, one is prime and one is not, but they both ran through the same filters with the same results. While all these divisibility tests are plenty neat, none of them give results which are a sufficient condition for a number to be prime.

Edited November 3, 2011 by the tree

[Mystery111]

Okay I have to ask, where on earth did you make the leap between "not divisible by 3" and "probably a prime"?

 

If we pick a couple of numbers, we can run them through any amount of divisibility tests.

 

Try 1921 and 2311 for utterly contrived examples.

 

• The last digit in both cases is odd.
  They've failed the divisibility test for 2 - does that make them both prime?
• The sum of all digits in both cases is not divisible by 3.
  They've failed the (your?) divisibility test for 3 - does that make them both prime?
• The last digit in both cases is not 0 or 5.
  They've failed the divisibility test for 5 - does that make them both prime?
• The last digit, subtracted from the rest of the number, is not divisible by 7 in either case.
  They've failed the divisibility test for 7 - does that make them both prime?
• The sum of every second digit minus the sum of the remaining digits, is not divisible by 11.
  They've failed the divisibility test for 11 - does that make them both prime?

 

As it happens, one is prime and one is not, but they both ran through the same filters with the same results. While all these divisibility tests are plenty neat, none of them give results which are a sufficient condition for a number to be prime.

 

 

I don't know what you're talking about. Do you actually understand what I am doing in the OP?

[the tree]

Clearly yes, you are getting over excited about the second of the divisibility tests mentioned, that is all.

[Mystery111]

I'm far too tired to have this discussion right now.

[the tree]

There's no rush. It's a forum not a chatroom. Maybe read up modular arithmetic or something.

[Mystery111]

Ah bugger it, for queen and country. And for the loudmouths.

 

I found that the [math]3^{3}[/math] table contains a very important pattern that could be pivotal to calculating the connection between primes.

18

27

36

45

54

63

72

81

 

Which when each individual number is subtracted gives

 

1-8 = 7

2-7 = 5

3-6 = 3

4-5 = 1

5-4 = 1

6-3 = 3

7-2 = 5

8-1 = 7

 

Instead of the pattern occuring at the exact value of [math]3^{3}[/math] it is deterred until the second appearance. This seems like a mathematical analogue of the prime number pattern. It may be applied to the mathematical foundation of the OP, which I will be testing soon. I am likely to spend many hours on this. I enjoy puzzles.

Edited November 3, 2011 by Mystery111

[the tree]

I found that the 3³ table [...] 18,27,36,45,54,63,72,81...

That would almost certainly be the 9 times table, or the 3² times table. But let's forgive that.

 

The differences between the digits start off hinting a sort of oscillating pattern indeed but urm... that doesn't really continue unfortunately.

 

9

7

5

3

1

1

3

5

7

9

0

2

4

6

8

 

I think that's what we'd call a good attempt. But you're not going to get further until you admit to yourself that this has more to do with the behavior of the number 3 in base 10, than it does any other prime or any general case.

Edited November 4, 2011 by the tree

[Mystery111]

Sorry, typo.

 

I pasted and copied too.

 

It is true though, it is not a continuous analogue of the prime numbers. You must however question when it happens.

[the tree]

Yeah, no, pretty much every pattern that comes up in modular arithmetic - even if it isn't very interesting, will have some kind of aesthetic appeal to it. Which is why I'm so certain that you should try actually learning some of this stuff rather than just speculating about it. Start learning about the Chinese Remainder Theorem or Fermat's Little Theorem, start devising your own proofs for how that damned divisibility check works (and probably, some point along the line, learn what a mathematical proof is), seriously, just, go learn something.

[baric]

It is interesting to note that no prime number will do this, and curiosly except the one appearance of 3 itself, the second prime number. There will be a reason why 3 begins there and causes this pattern throughout, and I called it a law because it is a true statement of all prime numbers.

 

No, it is NOT a law of prime numbers.

 

It is an artifact of using base-10 to represent numbers. If you used base-5, for example, your "law" would no longer work.

 

And since base-10 is just a human preference for displaying numbers, it cannot be a requirement for any mathematical law.

 

• The last digit, subtracted from the rest of the number, is not divisible by 7 in either case.
  They've failed the divisibility test for 7 - does that make them both prime?

I am not familiar with this technique.

 

Can you demonstrate how it works on the following multiples of 7?

 

 

14, 91, 133

[the tree]

Shoddy copy pasting on my part, sorry. Double the last digit, then subtract it from the rest.

Edited November 4, 2011 by the tree

[baric]

Shoddy copy pasting on my part, sorry. Double the last digit, then subtract it from the rest.

 

oh, that makes sense Thanks!

[DrRocket]

If the sum of the digits of any number are divisible by three then the number itself is divisible by three, you learn this at school and I believe it has been known since antiquity.

 

Proof

 

[math] 10 \equiv 1 [/math] (mod 3)

 

QED

Edited November 5, 2011 by DrRocket

[baric]

Proof

 

[math] 10 \equiv 1 [/math] (mod 3)

 

QED

 

I agree completely!

 

Unfortunately, the intended audience for this proof would not understand why you chose 10, that funny triple-equals symbol, or a 1. They might not even understood QED!

[the tree]

No need to patronise the OP, the privilege of education doesn't make you any better than them - and just because they're a little misdirected that doesn't give you the license to be a dick about it.

[baric]

No need to patronise the OP, the privilege of education doesn't make you any better than them - and just because they're a little misdirected that doesn't give you the license to be a dick about it.

 

If that was directed at me, I would like to point out that proficiency in mathematics specifically requires the "privilege of education". There have been many courteous attempts to explain to the OP why this discovery is not as significant as he would like to believe -- to correct his "misdirection", as it were.

 

Tailoring your answer to the education level of the questioner is not patronizing. It's teaching.

[Mystery111]

I agree completely!

 

Unfortunately, the intended audience for this proof would not understand why you chose 10, that funny triple-equals symbol, or a 1. They might not even understood QED!

 

I use symbols like that all the time you condescending prick. I am a physics student.

[baric]

I use symbols like that all the time you condescending prick. I am a physics student.

 

/hug

 

I tried several times to explain very simply why your "law" was just an artifact of our base system. Dr Rocket presented a proof demonstrating the same thing.

 

Was his proof sufficient, or do you still feel that this discovery is a "Law of Primes"?

[mooeypoo]

I use symbols like that all the time you condescending prick. I am a physics student.

 

!

Moderator Note

Tone it down, physics student, you're not representing your community too well with this attitude. Nor are you in accordance with our rules.

[Appolinaria]

Mystery took all of your responses into consideration, and never implied anything insulting.

 

You can point out error without making someone feel inadequate.

[baric]

Mystery took all of your responses into consideration, and never implied anything insulting.

 

You can point out error without making someone feel inadequate.

 

Well, that was never my intent and I apologize for any offense. I can only judge someone's proficiency in a subject by the content of their posts. If I were asking physics questions, I certainly hope that someone would talk down to my more basic level of understanding and would not consider it condescending. The OP seemed stuck on the supposed significance of summing digits and even referenced Vedic mathematics, of all things, so I was actually trying to lightly chide our illustrious Dr. Rocket for perhaps posting over the OP's head.

[Appolinaria]

Well, that was never my intent and I apologize for any offense. I can only judge someone's proficiency in a subject by the content of their posts. If I were asking physics questions, I certainly hope that someone would talk down to my more basic level of understanding and would not consider it condescending. The OP seemed stuck on the supposed significance of summing digits and even referenced Vedic mathematics, of all things, so I was actually trying to lightly chide our illustrious Dr. Rocket for perhaps posting over the OP's head.

 

Yeah. Understood.

[Mystery111]

Well, that was never my intent and I apologize for any offense. I can only judge someone's proficiency in a subject by the content of their posts. If I were asking physics questions, I certainly hope that someone would talk down to my more basic level of understanding and would not consider it condescending. The OP seemed stuck on the supposed significance of summing digits and even referenced Vedic mathematics, of all things, so I was actually trying to lightly chide our illustrious Dr. Rocket for perhaps posting over the OP's head.

 

Oh but I do. I talk to people on a level they can understand but equally without making them feel degraded in anyway.

 

You're either a bad teacher, or a bad liar.

[mooeypoo]

!

Moderator Note

If it wasn't clear, my note might have pointed at a specific person, but it was meant for everyone. Baric, stop condescending. Mystery, tone things down. The rest of you, if you think someone is misbehaving, use the 'report' button so we can regain control in a civil manner rather than let the subject shift from the actual question posed to arguments about who has the biggest potty mouth.

Get back on topic, guys, and be civil.

[PeterJ]

I sympathise with Mystery 111 since I have also spent a lot of time in the past as a complete mathematical dunce investigating the primes . I'm not even clever enough to be a physics student.

 

What I don't understand is what people keep talking about the primes like they are random or unpredictable. Mystery does it here, talking about chance, and even people like Du Sautoy do it. A layman is likely to take this as meaning it's pot luck where they appear. All it means, surely, is that we don't have a neat algorithm for predicting them. This does not mean they are unpredictable or mysterious.

Edited March 8, 2012 by PeterJ