Number theory question

[Gopfi]

Find all natural n for which every number written using n-1 one and one seven is Prime. (For example, the number 1711 is not one of them, because it is 29*59).

 

[Deleted member 4993]

Find all natural n for which every number written using n-1 one and one seven is Prime. (For example, the number 1711 is not one of them, because it is 29*59).

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Steven G]

Find all natural n for which every number written using n-1 one and one seven is Prime. (For example, the number 1711 is not one of them, because it is 29*59).

Exactly why am I going to do this?

I am also a bit confused. I assume that 1711 is n. But this makes no sense. I would think that n=4 since 1711 has 4-1=3 ones and one 7. So we rule out 4, not 1711.

 

[JeffM]

@Jomo

Based on the example, I think what is meant is that x is an integer expressed in decimal numerals using n - 1 "1" symbols and one "7" symbol.

So for n = 4, the relevant numbers are 1117, 1171, 1711, and 7111. In which case, that 1711 is composite is relevant.

Of course, I may be wrong. The question is obscure.

PS I see no reason a priori to believe the answer is finite.

 

[Gopfi]

I think for n = 3k there is no solution because number will divide by 3, also i reminded that number with 6k one will divide by 7 so n = 7k will divide by 7.

 

[Steven G]

@Jomo

Based on the example, I think what is meant is that x is an integer expressed in decimal numerals using n - 1 "1" symbols and one "7" symbol.

So for n = 4, the relevant numbers are 1117, 1171, 1711, and 7111. In which case, that 1711 is composite is relevant.

Of course, I may be wrong. The question is obscure.

PS I see no reason a priori to believe the answer is finite.

When the OP states For example, the number 1711 is not one of them doesn't that mean that 1711 is not one of the natural n for which every number written using n-1 ones and one seven is Prime? Doesn't really matter anyways as we understand the problem.