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There's http://oeis.org/A007530 with the least prime being 8 less than the fourth prime. Then there's one with the difference being greater, as in 211,223,227,229. Do you think there are more of the former than of the latter?

J. M. Bergot
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  • Up to $10^{10}$ there are slightly more of the latter (p,p+12,p+16,p+18) than the former (p,p+2,p+6,p+8). At $10^{11}$ it's back to a tiny lead by the former. – DanaJ Dec 12 '17 at 23:12
  • The example was simply to show an alternative to quadruplets like 11,13,17,19 and it need NOT have the first term differing from the last term by 18. One could easily have the three differences between the four terms each ending in order with last digits 1,3,7,9 to be a great variety. Hence, the latter would have vastly more terms than the original quadruples. One could try running the program allowing the differences of these three terms to be ANY numbers whatsoever. – J. M. Bergot Dec 13 '17 at 19:20
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    Further allowable examples: 461,463,467,479 and 202231,202243,202277,202289. – J. M. Bergot Dec 13 '17 at 19:33

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