Here :
http://www.math.ubc.ca/~bennett/BeGa-data.html
there is a complete list of the integral points of the Mordell-curves for $-10^7\le n\le 10^7$. I searched for large solutions (in particular for large solutions on curves with only $2$ integral points) and accidently found the following unusual gaps :
779996 2 [170,2386] [170,-2386]
787577 4 [256074644,4097791586581] [256074644,-4097791586581] [1778,74977] [1778,-74977]
794610 2 [253686159,4040593486767] [253686159,-4040593486767]
798736 2 [192536904,2671597178300] [192536904,-2671597178300]
800004 2 [-92,146] [-92,-146]
If I understand the database right, there are only the $5$ given numbers in the range $[779996,800004]$ , for which the Mordell-curve has an integral point. I did not check the whole list, but these gaps seem to be very large in comparison with the other gaps I noticed.
Is there an explanation that this range has such a small number of $n$'s with integral points ? Or could this indicate an error with the database ?
This error is now fixed. The file was apparently corrupted while converting from text to pdf. Thank you again for pointing this out (I will check the other files).