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


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#1 Rajnish Kaushik

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Posted 5 January 2014 - 04:05 PM

1-Even number

2-Prime number

3-Not prime

4-Non of these

Please explain yor answer


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#2 imatfaal

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Posted 5 January 2014 - 05:15 PM

1-Even number

2-Prime number

3-Not prime

4-Non of these

Please explain yor answer

 

 

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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#3 Strange

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Posted 5 January 2014 - 05:23 PM

It is obviously not even. And probably not prime.

 

In fact, not prime: http://www.wolframal...111111111 prime


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#4 imatfaal

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Posted 5 January 2014 - 05:34 PM

It is obviously not even. And probably not prime.

 

In fact, not prime: http://www.wolframal...111111111 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


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#5 Strange

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Posted 5 January 2014 - 05:35 PM

Please explain yor answer

 

Please explain your question! :)


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#6 Rajnish Kaushik

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Posted 6 January 2014 - 03:28 AM

thanks friends


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#7 deesuwalka

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Posted 6 October 2016 - 07:32 AM

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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#8 renerpho

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Posted 8 October 2016 - 04:32 PM

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, 8 October 2016 - 04:34 PM.

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#9 imatfaal

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Posted 10 October 2016 - 07:55 PM

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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