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**noobard****Member**- Registered: 2009-06-07
- Posts: 28

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

Everything that has a begining has an EnD!!!

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,410

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.

Character is who you are when no one is looking.

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**noobard****Member**- Registered: 2009-06-07
- Posts: 28

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

Everything that has a begining has an EnD!!!

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**Avon****Member**- Registered: 2007-06-28
- Posts: 80

A result related to this discussion is the following:

Suppose

If is prime then

**Proof**

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

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

Now so and so is not prime.

Hence if is prime then

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.Offline

**noobard****Member**- Registered: 2009-06-07
- Posts: 28

nice one !!!!

Everything that has a begining has an EnD!!!

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**DarkLightA****Member**- Registered: 2009-05-27
- Posts: 16

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

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**noobard****Member**- Registered: 2009-06-07
- Posts: 28

DarkLightA wrote:

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

Everything that has a begining has an EnD!!!

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**soroban****Member**- Registered: 2007-03-09
- Posts: 452

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