Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2009-06-09 14:40:37

noobard
Member

Offline

### 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

Everything that has a begining has an EnD!!!

## #2 2009-06-09 14:48:06

ganesh
Moderator

Offline

### 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.

Character is who you are when no one is looking.

## #3 2009-06-09 18:30:57

noobard
Member

Offline

### 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 ....  :-|

Everything that has a begining has an EnD!!!

## #4 2009-06-10 08:17:03

Avon
Full Member

Offline

### 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.

## #5 2009-06-10 13:35:08

noobard
Member

Offline

### Re: 7*11*13!!!

nice one !!!!

Everything that has a begining has an EnD!!!

## #6 2009-06-10 16:38:40

DarkLightA
Member

Offline

### 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.

## #7 2009-06-10 18:45:34

noobard
Member

Offline

### Re: 7*11*13!!!

#### 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!!!

soroban
Power Member

Offline

. .

. .

. . .

. .

.

. .

.