I've been wrestling with an induction. I think this'll work:


We must show is divisible by 11.

In other words,

Let k=1 and we get .

Base case is true. Now, we must show the induction step.

Let:





=

Add and subtract 10^2:

=

=

is divisible by 11 and so is 99.

Therefore, QED and all that.

This proof works if we have an even number of 0s, since 10^(2k+1) + 1 will always give you an even number of 0s, e.g.. 1001, 100001...
What about if there's an odd number of 0s, i.e. Prove the formula
(10^(k+1))^2 + 1 is not prime for k > 1

Look again. 2k+1 is an odd integer. The proof is sound.

I'm really curious about why my months old post about only 101 being prime matters to anyone.

Quote:

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Originally Posted by Wolfie1963

I need to find 2 prime numbers that, if multiplied, would generate a 400-digit number. Any idea how to go about this. I have all the prime numbers but no matter what I do I do not get 400. Am I looking at this question wrong maybe?
Thanks ::confused:

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Do you go to itt tech?? I have this same question and there's 4 or 5 of us working on it and have yet to find an answer myself..

Did anyone ever find the answer? I'm going to itt tech, and I have to solve this also. Any help would be greatly appreiciated

I have found one, there is a program you can down load free at:Mersenne Primes: History, Theorems and Lists you can visit:Math Forum - Ask Dr. Math for instructions on use...