# The number 11111..111111..11 (91)times is an?

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1-Even number

2-Prime number

3-Not prime

4-Non of these

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1-Even number

2-Prime number

3-Not prime

4-Non of these

Not even and not prime. It is divisible by 1,111,111 amongst others

If R_n is the number 1....1 with n repetitions then it can be shown that if n is not prime (ie can be divided by a and b) then R_n is not prime and that R_n can be divided by R_a and R_b

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It is obviously not even. And probably not prime.

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It is obviously not even. And probably not prime.

I had forgotten about wolfram alpha - it can give me the actual result to my divisor 1,111,111

1000000100000010000001000000100000010000001000000100000010000001000000100000010000001 x 1111111

That is such a cool looking sum; and if you think about it - the pattern makes total sense

thanks friends

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• 2 years later...

1. It's not an even number because it ends with 1, it's an odd number

3. It's not a prime number because it's divisible by 1,111,111 other than 1

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Primes of that form are are quite rare, see https://oeis.org/A004023 to find numbers of the form $111 \dots 111=\frac{10^n-1}{9}$ that are prime.
It turns out that this number is prime for n=2, 19, 23, 317, 1031, 49081, 86453, 109297 or 270343.

Edited by renerpho
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Primes of that form are are quite rare, see https://oeis.org/A004023 to find numbers of the form $111 \dots 111=\frac{10^n-1}{9}$ that are prime.

It turns out that this number is prime for n=2, 19, 23, 317, 1031, 49081, 86453, 109297 or 270343.

Gotta love Sloane's. I hadn't realised they were so rare - just that it was relatively simple to show if the number had to be compound; obviously it is always simpler to show that a number is compound than to show that it is prime but in this case the test to show compound nature was so cute.

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