Quote:
Originally Posted by robert44444uk
In the first 896 6interprimes, 2 are 1mod3 (3565765570 and 9032233630), 4 are 2mod3 (10273573520, 156990740, 8636267360, 9257290415) and the other 890 are 0mod3.
Not really understanding why

One observation: If N is an interprime, N is not divisible by 3, and the smallest prime in the interval is greater than 3, then
all the gaps must have length divisible by 3.
For if N =/= 0 (mod 3), p is one of the primes, p =/= N (mod 3), and p =/= 0 (mod 3), then the symmetrically located number 2*N  p will be == 0 (mod 3).
This condition might narrow things down a bit.