Another Question Via Email

MathsIsFun · 2005-12-16 20:38:22

(I received this Q via email from "santhoshkumar". I have replied pointing to this post, so hopefully they will come along and clarify a bit!)

Respected sir /madam .i am guy form India ,I
want to know when does the prime number comes .after what time of
number does the prime number comes .I found in web site that all
the prime number comes after or number divisible by 6.expect
2&3.are try to send me how does the next number comes after what
type number does the number come in given sum below I will be very
use full if u do this for me or try guide me whom to contact by
web or e-mail I am very poor to by some costly book or try to work
out and send me with an example for give some which I got by mail

krassi_holmz · 2005-12-16 21:08:50

All the prime numbers greater than 3 are from the type

and from the type

Last edited by krassi_holmz (2005-12-16 21:09:57)

krassi_holmz · 2005-12-16 21:28:46

When I think for a while, I found an interesting fact:
The question is
Which remainders by K suppose that p is eventually prime?
So, if tru
If a number is from the form

if GCD[K,G]>1 then L is truely non-prime.
So, if all prime, greater than K are from the form

then for all 1<i<K-1 GCD[i,K]>1
Let find the chain of K-s
The firs member is 4:
GCD[4,2]=2
The second is 6:
GCD[6,2]=2
GCD[6,3]=3
GCD[6,4]=2
Is there third?
I think there isn't.
Here's what have to be prooved:
There isn't number H greater than 6 for such every prime numbers, greater or equal to H-1 are from the form

Last edited by krassi_holmz (2005-12-16 21:50:04)

r.santhoskumar · 2005-12-18 20:24:21

krassi_holmz wrote:

All the prime numbers greater than 3 are from the type

and from the type

try to give an example of ur answer . iwll be very use full if u do this .i aslo need that when does the prime number comes .after what type of number does the prime number comes.

MathsIsFun · 2005-12-18 21:38:57

Hi Santhos. Glad you arrived here. Now we can discuss primes with you.

Primes are actually hard to predict, and you can't use the formulas p=6i±1 or p=4i±1 to find them. But every prime does have those two properties.

For example, 37 is a prime. It is 6×6+1, but there is no prime at 6×6-1 (=35, which is not prime).

We have a short list of prime numbers, and a useful Prime Factorization Tool. You can use that tool to check to see if a number is prime or not (if a number cannot be factored it is prime)

Jai Ganesh · 2005-12-18 23:05:07

Hi r.santhoskumar,
I am sure those two links would be helpful.
Here's another bigger list of Prime numbers and more about Prime numbers.

John E. Franklin · 2005-12-20 17:14:11

A five minute analysis on a number line reveals that p=6i±1, and the equation with the 4 is not needed.

krassi_holmz · 2005-12-23 08:14:03

And for my problem:I prooved that ther there isn't third number. That means that for number k greater than 6 there exist prime number p that is not from the form ik +- 1.

santhoshkumar · 2005-12-29 19:48:37

krassi_holmz wrote:

All the prime numbers greater than 3 are from the type

and from the type

how can i send u attachment of my question to u in this post

santhoshkumar · 2005-12-29 19:55:29

santhoshkumar wrote:

krassi_holmz wrote:
All the prime numbers greater than 3 are from the type

and from the type
how can i send u attachment of my question to u in this post

If there are images in this attachment, they will not be displayed. Download the original attachment

Respected sir /madam .i am guy form India ,I want to know when does the prime number comes .after what time of number does the prime number comes .I found in web site that all the prime number comes after or number divisible by 6.expect 2&3.are try to send me how does the next number comes after what type number does the number come in given sum below I will be very use full if u do this for me or try guide me whom to contact by web or e-mail I am very poor to by some costly book or try to work out and send me with an example for give some which I got by mail

."Dr. Richard Botting" <Dickinson@csci.csusb.edu> wrote:

Thank you for your message.

Forgive me if I misunderstand it, I found it hard to
read.... my mail program may have removed some of the formatting.

I am only an amateur in Number Theory. I have
found that the following book very helpful and a continuing
pleasure to return to:
From Zero to Infinity: what makes numbers interesting
by Constance Reid
(Many editions... look in libraries and 2nd hand book stores,
or $7 (used) on amazon.com).

Let me see if I have understood your question.
It helps if we use algebra to clarify what we want to say.

Suppose we have a prime `p`, what can we say about `p-1` and
`p+1` the numbers before and after `p`.

Well if `p` is greater than 2 then it will not be divisible by 2.
It has to be odd. There must be a remainder when we divide
by 2. And this remainder has to be 1.

So
p = 2*n+1
for some number n=1,2,3...

So:
p-1 = 2*n

So p-1 is divisible by 2.

More
p+1 = 2n+1+1 = 2*n+2 = 2*(n+1)
another even number.

So: Each prime p>2, is surrounded by two even numbers.

Now consider 3. Each prime p > 3 can not
be divisible by 3. There must be a (nonzero) remainder.

This reminder is either 1 or 2.

So, either
p = 3*n+1 or p=3*n+2 for some n:1..

So either
p-1=3*n or p+1 = 3*n+3 = 3*(n+1)

So either p-1 or p+1 is divisible by 3.

But both p-1 and p+1 are divisible by 2.

So either p-1 or p+1 is divisible by 6.

MORE: consider 4: p-1 and p+1 are both even and p+1 = (p-1)+2,
so one of these two numbers is divisible by 4.
(the multiples of four are every other multiple of 2: 2,4,6,8,10,12,...)

SO: each prime has a multiple of 4 on one side or the other,
as well as a multiple of 6.

Is there a more general property.... about multiples of 5,7,11, ...

Perhaps. I'm no expert. But consider a number n
and a prime p that is larger than 2*n, then we know
that
p = n*q+r for some q>1 and r:1..(n-1).
So (visualize the numbers in line with n*q+1, n*q+2, ....n*q+(n-1)
sliding below them...)
either n*q or n*(q+1) is within n/2 of p.

(I guess)
Example: each prime>14 is within 4 of a multiple of 7.

That's about as far as I can go.... I think more complex
patterns need some complicated Number Theory.

I hope this helps.... don't lose the interest in numbers.
They are an endless comfort and distraction... and occasional
source of fun.

RJBotting

PS. I may wewrite this answer a bit and post it on
my web... can I quote your name or EMail??

RJB

sir try to send me with a example i will be very use full.if u do this 4 me

9 3 0 9 3 7 3
4 6 4 7 2 6 5
5 7 7 9 0 9 1
0 4 5 9 3 3 5
5 2 9 5 9 9 1
0 2 3 5 8 4 4
3 9 9 4 7 4

2 4 8 9 6 8 1
1 7 7 1 1 9 8
0 1 6 7 4 6 8
8 3 0 3 8 3 6
9 8 9 5 6 1 2
1 3 5 2 6 0 1
6 4 2 5 8 4 3

2 3 9 0 2 3 6
1 0 9 7 7 1 9
9 5 4 3 1 3 1
5 1 0 5 4 9 9
0 8 7 0 5 9 5
8 0 9 5 6 3 9
5 6 7 4 9 5 0

A colleague has kindly supplied the following when a number is divided by 6 we get a quotient and then a remainder between 0 and 5. The numbers of the form 6n or 6n+4 = 2(3n+2) cannot be prime. The numbers of the form 6n+2 are divisible by 2 and so only 2 occurs as a prime here. Similarly numbers of the form 6n+3 are divisible by 3 and only 3 occurs as a prime. So primes larger than 3 have either the form 6n+1 or the form 6n+5. The first are 1 more than 6n while the second are 1 less than 6(n+1).

krassi_holmz · 2005-12-29 19:56:54

I think you can't Bur wait for MathsIsFun.

krassi_holmz · 2005-12-29 20:06:53

Sorry, santh, first time i didn't saw your last post. It's pretty good. And something interesting.
Conjecture:
Let p-prime.
Then for every k∈[1,p) there exist prime number q>p for such
q==k(mod p)

I'll test it using computer program.

Last edited by krassi_holmz (2005-12-29 20:08:34)

krassi_holmz · 2005-12-29 20:38:50

My conjecture is true.

krassi_holmz · 2005-12-29 20:42:33

http://mathworld.wolfram.com/topics/PrimeNumbers.html

santhoshkumar · 2006-01-20 02:25:21

krassi_holmz wrote:

My conjecture is true.

why no reply for my question try to send me an example for ur answer please i will be very use full if u do this ok

santhoshkumar · 2006-02-07 23:02:14

my question is that when does the prime number comes in above number which i have post in above .please try to post me with the answer and an example. i m very thank for ur 6i +/-.

kempos · 2006-02-08 02:14:15

i don't think it's possible to predict when there will be a prime number. but might be wrong :-(

santhoshkumar · 2006-02-09 00:26:59

kempos wrote:

i don't think it's possible to predict when there will be a prime number. but might be wrong :-(

try to find that how that primernumber comes in above number atleast trt to find that how to find even a single prime number or any number comes after what type of number i will be very use full if u do this

santhoshkumar · 2006-02-15 22:47:51

santhoshkumar wrote:

kempos wrote:
i don't think it's possible to predict when there will be a prime number. but might be wrong :-(
try to find that how that primernumber comes in above number atleast trt to find that how to find even a single prime number or any number comes after what type of number i will be very use full if u do this

try to find any number that how does the number come in this number comes abovein last post what ever it may be even or odd or pirmenumber or anyone number 1,2,3,4,5,6,7,8,9,0 what evryit may i need that how that number comesafter what type of number doesit come i will be veryusefull if u do this

r.santhoshkumar · 2006-04-08 19:36:59

ganesh wrote:

Hi r.santhoskumar,
I am sure those two links would be helpful.
Here's another bigger list of Prime numbers and more about Prime numbers.

sir kindly tell me that how can i find that next number is prime......i got an answer that all prime numbers comes after or befor a number divisible by6 expect 2,3 ...this is true for some time not for all the times... try to help me

MathsIsFun · 2006-04-08 20:42:20

Yes, but just because you always see fish in water, does not mean that every time you see water there will be fish

The primes are a bit like fish too. When you find one you recognise it (in the case of primes you test to make sure they have no prime factors). But you don't always find them where you expect.

santhoshkumar · 2006-05-09 19:12:48

MathsIsFun wrote:

Yes, but just because you always see fish in water, does not mean that every time you see water there will be fish
The primes are a bit like fish too. When you find one you recognise it (in the case of primes you test to make sure they have no prime factors). But you don't always find them where you expect.

i have question that how can i make match all the odd number form 1 to 80 there are total 40 odd numbers
i want all the odd numer in1 row form example

1,3,5,7,9,11,13,15,17,19
but i want to match all the number odd numbers with one row from 1 to 80 how may rows it will take i want to make it in simple way . try to say me that i want to make with 150 rows can i do that

r.santhoshkumar · 2006-05-11 00:55:09

MathsIsFun wrote:

Yes, but just because you always see fish in water, does not mean that every time you see water there will be fish
The primes are a bit like fish too. When you find one you recognise it (in the case of primes you test to make sure they have no prime factors). But you don't always find them where you expect.

i have question that how can i make match all the odd number form 1 to 80 there are total 40 odd numbers
i want all the odd numer in1 row form example

1,3,5,7,9,11,13,15,17,19
but i want to match all the number odd numbers with one row from 1 to 80 how may rows it will take i want to make it in simple way . try to say me that i want to make with 150 rows can i do that

santhoshkumar · 2006-05-11 01:06:43

[ i have question that how can i make match all the odd number form 1 to 80 there are total 40 odd numbers
i want all the odd numer in1 row form example

1,3,5,7,9,11,13,15,17,19
but i want to match all the number odd numbers with one row from 1 to 80 how may rows it will take i want to make it in simple way . try to say me that i want to make with 150 rows can i do that

r.santhoshkumar · 2006-05-12 01:11:34

r.santhoshkumar wrote:

MathsIsFun wrote:
Yes, but just because you always see fish in water, does not mean that every time you see water there will be fish
The primes are a bit like fish too. When you find one you recognise it (in the case of primes you test to make sure they have no prime factors). But you don't always find them where you expect.
i have question that how can i make match all the odd number form 1 to 80 there are total 40 odd numbers
i want all the odd numer in1 row form example
1,3,5,7,9,11,13,15,17,19
but i want to match all the number odd numbers with one row from 1 to 80 how may rows it will take i want to make it in simple way . try to say me that i want to make with 150 rows can i do that

why no reply for my question

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