To focus the discussion somewhat back to my original query, I did work on this last year: http://chesswanks.com/pxp/weeksbetweeneasters.html My empirical brute-force approach was able to snapshot a couple of hundred instances out of the maximum 2850000 required for a definitive solution. I had hoped that a theoretical understanding of the Gregorian Easter algorithm might somehow shortcut thereto but perhaps brute-force is all that is possible with this particular arithmetic.
When two separate Easters are one year apart, they can be 50, 51, 54, or 55 weeks apart. When they are 3 years apart, there are 5 weekly possibilities. When they are 10 years apart, there are 6 weekly possibilities. When they are 125 years apart, there are 7 weekly possibilities. Can there ever be 8 weekly possibilities?