A Law of Primes

[Mystery111]

I discovered a Law for Prime Numbers.

 

I have for the couple of years searched ways of finding a law which will determine the prime numbers. As we all know, the law which will allow us to predict prime numbers are unknown. Unfortunately, today, I cannot still offer any remarkable law which will determine prime numbers, but I did find another law for prime numbers along the way.

 

The Law States: The sum of all numbers which make up a prime will give you a number which will never be allowed to be a multiple of 3, nor do any digits ever make the sum of 12 to allow 3 to be divided, with the only acception of the the second prime number that is 3. If after you have taken the sum of all your numbers and you end up with a two-digit number, you continue taking the sum of the value until you have only one number left.

 

I have taken this law up to the 2000th prime number, and by finding this I have never been so sure that there is in fact a hidden structure behind their appearances.

[imatfaal]

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. To find out if the sum of your digits is divisible by three you can repeat the process - this explains the second part of your law.

 

You could make similar exclusionary statements for all of the division rules - so sorry, not a new law, not really a law at all

[CaptainPanic]

As imatfaal says: it's not so new. But it is quite nice that you found out yourself.

[baric]

I discovered a Law for Prime Numbers.

 

I have for the couple of years searched ways of finding a law which will determine the prime numbers. As we all know, the law which will allow us to predict prime numbers are unknown. Unfortunately, today, I cannot still offer any remarkable law which will determine prime numbers, but I did find another law for prime numbers along the way.

 

 

Just so you are aware, these digit summation rules will all help you rule out certain numbers for primality. They work because we use base-10 to represent numbers:

 

Because 2 & 5 are factors of 10:

 

If the final digit of a number is 0,2,4,6 or 8, then that number is divisible by 2.

 

If the final digit is 0 or 5, then that number is divisible by 5.

 

Because 9 & 11 are adjacent to 10:

If the digits of a base-10 number add up to a multiple of 9, then that number is divisible by 9. Since 3 is a factor of 9.. if they are a multiple of 3, then the number is divisible by 3.

 

If the sums of alternating digits are the same (ex: 583), then that number is divisible by 11.

 

I hope that helps.

 

You can write numbers out in different bases and verify that these same rules apply.

[Mystery111]

It is kinda new, because no one has discovered this ''nature'' behind the primes. I was well aware of the division rule by the way

[baric]

It is kinda new, because no one has discovered this ''nature'' behind the primes. I was well aware of the division rule by the way

 

But it's not really a "law" of primes as it is dependent upon representing the numbers in base-10. It doesn't work in base-5, for example.

[Mystery111]

It is surely not being suggested that the prime numbers have this feature by accident surely? The fact the prime numbers exhibits this pattern is due to some inherent mathematical factor. I was close to saying a numerological factor there... but I think it is deeper than that.

[Appolinaria]

It is surely not being suggested that the prime numbers have this feature by accident surely? The fact the prime numbers exhibits this pattern is due to some inherent mathematical factor. I was close to saying a numerological factor there... but I think it is deeper than that.

 

Sounds intriguing. I believe absolutely everything contains a pattern, some are just too complex for us to perceive.

[Mystery111]

Sounds intriguing. I believe absolutely everything contains a pattern, some are just too complex for us to perceive.

 

If there is a pattern then in theory prime numbers have a rule which will let us determine their appearances... I hope so atleast!

[Appolinaria]

If there is a pattern then in theory prime numbers have a rule which will let us determine their appearances... I hope so atleast!

 

In 1975, number theorist Don Zagier commented that primes both

 

"grow like weeds among the natural numbers, seeming to obey no other law than that of chance [but also] exhibit stunning regularity [and] that there are laws governing their behavior, and that they obey these laws with almost military precision."

 

http://www.dailymail...istics-PhD.html <--- view this link.

 

 

GO, MYSTERY, GO!

while you're at it, please sign this form confirming I'll make 50% of earnings for the crucial moral support I've supplied.

Edited November 2, 2011 by Appolinaria

[Mystery111]

Very true.

[Appolinaria]

Give me this formula my friend, so I can manipulate chance, and win the lottery an uncountable amount of times.... mwahaha.

[Mystery111]

It seems likely that the pattern I have uncovered for primes makes primes ''a certain class'' of numbers which fall within a rigid class of numbers which must pertain to the logic of the OP. Not all numbers can be given the division rule for the number three, which means that this significantly cuts down the broadness of their appearances but not limited to a simpler mathematical structure.

[doG]

It is surely not being suggested that the prime numbers have this feature by accident surely? The fact the prime numbers exhibits this pattern is due to some inherent mathematical factor.

Not really. Every 3rd number from 3 on is divisible by 3 and therefore composite. This also implies that all primes are adjacent to a number divisible by 3 as are all other numbers not divisible by 3. In general, all numbers greater than 3 that are not divisible by 3 are adjacent to a multiple of 3 whether they are prime or composite. There's no pattern in that unique to the primes.

[Mystery111]

Not really. Every 3rd number from 3 on is divisible by 3 and therefore composite. This also implies that all primes are adjacent to a number divisible by 3 as are all other numbers not divisible by 3. In general, all numbers greater than 3 that are not divisible by 3 are adjacent to a multiple of 3 whether they are prime or composite. There's no pattern in that unique to the primes.

 

What is being suggested however is that prime numbers are unique to stay away from numbers divisible by 3. No result of vadic calculation of a prime number will give you a value of 12 either. So whether you account that every 3rd number from 3 is divisible by 3 only just strengthens the hypothesis that it is a matter of a hidden variation of patterns inherent in prime numbers showing up. It surely then weakens the idea that prime numbers are by chance.

[doG]

What is being suggested however is that prime numbers are unique to stay away from numbers divisible by 3.

No they're not unique. Do you think primes stay away from numbers divisible by 3 any more than composite numbers like 10,14,16,18,20,22,26,etc.?

 

FWIW, you might be interested in Euler's 6n+1 Theorem. It's been around a long time which shows your premise is nothing new.

[Mystery111]

It is unique, and no I wasn't immediately aware of Eulers 6n+1 theorem. If this has been discovered before for prime numbers, I am happy I made the discovery independanly.

 

Mind you, I think I'm the first to express it this way

[imatfaal]

It is unique, and no I wasn't immediately aware of Eulers 6n+1 theorem. If this has been discovered before for prime numbers, I am happy I made the discovery independanly.

 

Mind you, I think I'm the first to express it this way

 

All you are saying is that numbers that are divisible by three cannot be primes - and that is part of the definition of a prime number

[the tree]

All you are saying is that numbers that are divisible by three cannot be primes - and that is part of the definition of a prime number

In other news, blue things are not red.

[doG]

In other news, blue things are not red.

Wow, that's as unique as the fact that primes are not divisible by 3

[Mystery111]

All you are saying is that numbers that are divisible by three cannot be primes - and that is part of the definition of a prime number

 

Vedic calculation will do this. Vedic is an Indian form of counting the sum values of the number in question. Say your number was 3398101 the sum value is 25, then the vadic value of this is 2+5 = 7 and that would mean it is a prime number because 3 cannot divide into this.

 

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.

[the tree]

Vedic calculation will do this. Vedic is an Indian form of counting the sum values of the number in question. Say your number was 3398101 the sum value is 25, then the vadic value of this is 2+5 = 7

That's known as a digital sum. The word vedic refers to pretty much any ancient hindi tradition but not a specific operation.

 

and that would mean it is a prime number because 3 cannot divide into this.

Except that 3398101=7³×9907, that is to say that it is not prime. All the digital sum has told you is that 3398101(mod3)=1.

 

There will be a reason why 3 begins there and causes this pattern throughout

Well it's because 10ⁿ(mod3)=1 for all n but I think somehow you've still missed what pattern we're talking about.

 

and I called it a law because it is a true statement of all prime numbers.

It's also true of EVERY OTHER NUMBER THAT IS NOT DIVISIBLE BY THREE. We're talking about two thirds of the integers that just happens to have the primes as a subset. Edited November 3, 2011 by the tree

[Mystery111]

That's known as a digital sum. The word vedic refers to pretty much any ancient hindi tradition but not a specific operation.

 

Except that 3398101=7³×9907, that is to say that it is not prime. All the digital sum has told you is that 3398101(mod3)=1.

 

Well it's because 10ⁿ(mod3)=1 for all n but I think somehow you've still missed what pattern we're talking about.

 

It's also true of EVERY OTHER NUMBER THAT IS NOT DIVISIBLE BY THREE. We're talking about two thirds of the integers that just happens to have the primes as a subset.

 

I see an order. Obviously you do not class it as important as I do.

[the tree]

The thing is, it's a really neat way of checking divisibility by 3. But getting over excited about the revelation that primes aren't divisible by three, is just going to make you look stupid especially if you're going to pick a composite number as your example.

[Mystery111]

I am not a fool, I am perplexed by design, and this is a designated pattern for primes. It has never been found before me, so it acts itself as an evidence there could be a pattern in their appearance. I don't understand your rejection, and this case I might be a fool.