What do I do when I get an “Iterator does not have appropriate bounds” error?

Question

I used this as input

Table[600851475143/i , {i, 1, 600851475143}]

but got an error

Table::iterb:Iterator {i,1,600851475143} does not have appropriate bounds.

But this gives me no error why?:

Table[600851475143/i , {i, 1, 13}]

Answer 1

This is because the number you used is extremely large. The number of iterations supported (in either Table or Do) seems to be $2^{31}-1$, i.e. the maximum size of a signed machine integer. I believe this is also an upper bound on the size of an array in Mathematica.

This limitation is not unreasonable: the size of the Table you are trying to construct is too large to fit into memory anyway. (Even if each element could be stored on a single byte, you'd be asking for 600 GB of memory.)

If you change the step size in the iterator to a large number, it will work:

Table[600851475143/i, {i, 1, 600851475143, 100000000}]

Answer 2

As Szabolcs has said the trouble lies in the size of the table you are trying to produce.

It does not however stop you plotting the function you want to investigate.

Plot[600851475143/i, {i, 1, 600851475143}]

Or sampling the function at discrete steps and then plotting it as in:

z=Table[600851475143/i, {i, 1, 600851475143, 10^6}];
ListPlot[z];