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.

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.

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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