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#1 2015-10-19 12:04:07
- Primenumbers
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- Registered: 2013-01-22
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A New Way Of Finding If "p" Is Composite.
p=any number ending in 3
check p is not a square
where a+b is a factor and a-b is another factor
if p is prime you will not find any factors
if p is composite you will find factors.
Example:
p=33
27*33=891
46+35=81=27*3 46-35=11
factors for 33 are 3 and 11
"Time not important. Only life important." - The Fifth Element 1997
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#2 2016-04-16 19:54:02
- thickhead
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Re: A New Way Of Finding If "p" Is Composite.
This can be disproved. if a and b are integers a+b and a-b are either both odd or both even. Therefore the product a^2-b^2 is either odd or divisible by 4. so if p is only divisible by 2 say 10 it is not possible to find a and b.( I mean 27p can be factorized into 2 odd or 2 even numbers.)
Last edited by thickhead (2016-04-16 19:56:35)
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#3 2016-04-22 21:07:29
- Primenumbers
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Re: A New Way Of Finding If "p" Is Composite.
Sorry, this theorem only works with ODD numbers. So p is odd and a is either odd or even and b is the opposite.
Another way of proving p is prime is;
only when a-b=1So add possible to p and see if it = a square.
(a+b) and (a-b) will be factors
This is because for any odd Non-Prime that has a factor of >1, it can be produced with the below formula;
I can prove it
x = (f + L)/2
y = (f - L)/2 therefore
minus the two and it = fL which are the two factors....
And x - y = ((f + L)/2) - ((f - L)/2) = L which must be >1 for p to Not be, Prime or 1.
Last edited by Primenumbers (2016-04-22 21:08:56)
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#5 2016-04-22 23:13:31
- thickhead
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Re: A New Way Of Finding If "p" Is Composite.
I am sorry. I had not noticed that p is a number ending in 3.
PRIME NUMBERS WROTE
" p= any prime number ending with 3. Check p is not a square." This is redundant. No square will end with 3.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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#6 2016-04-22 23:27:03
- Primenumbers
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Re: A New Way Of Finding If "p" Is Composite.
Of course p does have those possible squares. But ONLY those. To see if p is composite, test all values for b where b is greater than 1and smaller than (p - 1)/2.
"Time not important. Only life important." - The Fifth Element 1997
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#8 2016-04-23 00:39:04
- Primenumbers
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Re: A New Way Of Finding If "p" Is Composite.
I don't really know how to do this. 4k+2 will always be even so n will be any odd no. My formula doesn't work for even no.'s. So n has factors f and L where a=(f+L) /2 and b=(f-L) /2. For a prime the only factors will be 1 and itself, so the only occurrence for a squared minus b squared will be when a=(p+1)/2 and b=(p-1)/2. For a composite b will be less than this.
"Time not important. Only life important." - The Fifth Element 1997
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#10 2016-04-23 01:15:38
- Primenumbers
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Re: A New Way Of Finding If "p" Is Composite.
For a prime the only factors will be 1 and itself, so the only occurrence for a squared minus b squared will be when a=(p+1)/2 and b=(p-1)/2. For a composite b will be less than this.
"Time not important. Only life important." - The Fifth Element 1997
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#11 2016-04-23 03:04:37
- bobbym
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- Registered: 2009-04-12
- Posts: 109,606
Re: A New Way Of Finding If "p" Is Composite.
Hi;
I have received two complaints about this thread and that is three too many.
Tact is the art of making a point without making an enemy.
@Nehushtan: Please try to think of the other guys feelings when you respond. No more "rubbish" comments.
@Primenumbers: Please try to be more receptive when someone points out a possible error. Supposedly you are posting so that you can get feedback on your work. This is valuable to us all. Welcome criticism when you get it, this is how we all learn.
So I say, calm down everyone. Everyone knows the rules and everyone knows me.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2016-04-23 03:22:21
- googol
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Re: A New Way Of Finding If "p" Is Composite.
Every composite number is the difference of two squares, a prime is never:
In your example
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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#13 2016-04-23 04:03:58
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: A New Way Of Finding If "p" Is Composite.
@Nehushtan
Did you read post #11? Using Einstein to demean a member is clever but still not allowed. Please stop deleting your posts and my additions in those posts.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#14 2016-04-25 04:32:44
- Primenumbers
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- Posts: 149
Re: A New Way Of Finding If "p" Is Composite.
p=any number ending in 3
check p is not a square
where a+b is a factor and a-b is another factor
Number ending in 3: factors end in 1 and 3, or 7 and 9. Times by 27 factors now end in 1 and 1.
f=10c+1 L=10d+1
b=(10c+1-10d-1)/2=5(c-d)
Last edited by Primenumbers (2016-04-25 04:37:54)
"Time not important. Only life important." - The Fifth Element 1997
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