If you're intending to use only integers then I would give serious consideration to expanding the range from 1000 to something higher; an average of ten units between levels means that you'll either be too cramped to differentiate at the low end, or too close between levels at the high end. For instance, one fairly common way of spacing levels is to use quadratic growth: make the 'point count' of level n proportional to n2. This means that the gap between levels grows linearly: the number of points needed to go from level n to level (n+1) is (roughly) proportional to n. Unfortunately, if we try and fit this approach to your data, then to get level 100 at 1000 points, we need to take the constant of proportionality to be (1002) / 1000, or 1/10; in other words, the number of points needed for level n is n2/10. This works well at the high end: level 100 is at 1000 points, level 99 is at (992)/10 = 980 points, level 98 is at 960 points, level 97 is at 940.9 = 941 points, etc. Unfortunately, on the low end this means that the number of points for level 1 is 0, but the number of points for level 2 is (22)/10 = 0.4 = 0 also, then level 3 is at 1, level 4 is at 2, etc.
Another approach used is to go for exponential growth, where each level is some constant times the size of the previous. Unfortunately, over 100 levels this runs into similar and arguably even worse problems - to grow from 1 to 1000 over that span you'd need to multiply each number by 1000(1/100) = 1.0715, or 7% growth from level to level - this means that level 1 is at 1, level 2 is at 1.07 = 1, level 3 is at 1.15 = 1, ..., up to level 97=813 points, level 98=871 points, level 99=933 points, level 100 = 1000 points. This approach works better with a much smaller number of levels - for instance, over a span of roughly 20 or so levels.
If you have to go from 0 to 1000, then I would consider a hybrid approach; have the first few levels' growth be explicitly linear, then switch over to a quadratic growth rate somewhere around level 10 or so. You should be able to tune your parameter values so there's decent separation at both ends of the scale.