I have found the first occurrences of many of the missing gaps.

Code:

GAP after prime
41 181773281
55 72506501
113 51633731
160 78139751
167 46187831
172 45290801
174 23482001
181 33113651

I believe all gaps (except the obvious 2mod 7 and 5mod 7) are represented although a few that are 1 mod 7 and 6 mod 7 can sometimes be underrepresented.