Here is a version using GMP library to calculate CRT offsets, so it can go beyond maxprime 101:

primeinterval.c
No real maximum now, but it gets messy. I tested at the 1700 interval and already at maxprime=73 there are 11.5K solutions with minimum+2 and it finds more and more solutions if you continue to run min, min+1 and min+2 to higher values.

What is the best maxprime for 1700 interval? Then I can provide some CRT offsets, I did a full run to maxp=37 and ran the best solutions higher, but I'm not going to use them for any prime gap search.

I do not think we want to save min+3 and min+4 solutions like you suggested. I tested at 1700 maxp=29 and 1250 maxp=31 and there were 4.5K / 11K min+3 solutions and 25K / 111K min+4 solutions and running all those would take a very long time, and that would just give too many solutions at higher maxprimes.

I changed the way it resumes from earlier file. Instead of running it 2-3 times with the min value, min+1, min+2, you just run it once with the minimum value: (example 1700 maxp 37 minimum 231 running it to maxp=59):

**primeinterval.exe 59 primeinterval1700-37.txt 231**
It will test all the 231 solutions first and then continue automatically with the 232 solutions and 233 solutions and you can stop it at any time with CTRL+C if it takes too long, and use the best it found so far in the primeinterval1700-59.txt file.