Math Is Fun Forum

noobard

Member

Registered: 2009-06-07

Posts: 28

7*11*13!!!

We most of the times think that 1001 is a prime ...well it is not
it is a product of 7,11,13
so wen we see a 6 digit number abcabc then it is nothing but 1001*abc...and can be split into factors 7*11*13*factors of abc...
and hence can be analysed further

kp
enjoyin maths

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: 7*11*13!!!

noobard,
This fact is known to almost all mathematicians.
Here's another bit of information.
10001 is not a prime number, it is divisible by 73 and 137.

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noobard

Member

Registered: 2009-06-07

Posts: 28

Re: 7*11*13!!!

zzzzzzzzzz ganesh i thought being a new bee on this forum so started of with this ...........nice u told me that ....  :-|

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Everything that has a begining has an EnD!!!

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: 7*11*13!!!

A result related to this discussion is the following:

Suppose a and n are integers with

and

.
If

is prime then a is even and n is a power of 2.

Proof
Certainly a should be even, since if a is odd then

is even and not 2.

Suppose n = st where s is odd and s>1. Then

Now

so

and so

is not prime.
Hence if

is prime then n cannot have any odd divisor other than 1 so n is a power of 2.

It follows from this result that

is divisible by

so 1001 is divisible by 11.

Of course, ganesh's example shows that the converse of this result is not true since

is not prime even though 10 is even and 4 is a power of 2.

noobard

Member

Registered: 2009-06-07

Posts: 28

Re: 7*11*13!!!

nice one !!!!

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Everything that has a begining has an EnD!!!

DarkLightA

Member

Registered: 2009-05-27

Posts: 16

Re: 7*11*13!!!

Any number with an even number of digits that is a palindrome (same forwards and backwards, like 529925) is a multiple of 11.

noobard

Member

Registered: 2009-06-07

Posts: 28

Re: 7*11*13!!!

Any number with an even number of digits that is a palindrome (same forwards and backwards, like 529925) is a multiple of 11.

nice.. can be proved by divisibility rule for 11

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Everything that has a begining has an EnD!!!

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: 7*11*13!!!

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