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Old 2019-03-06, 17:04   #5
Dr Sardonicus
 
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Feb 2017
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Quote:
Originally Posted by robert44444uk View Post
In the first 896 6-interprimes, 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.
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