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The hardware and software on this system was updated September 4th.
Please let me know of any problem you encounter.
<caldwell@utm.edu>
There are exactly 9 gaps and 18 composites below 29 (the 10th prime number). Since 9 divides 18, we can say the average (or mean) gap less than 29 is 2, i.e., an integer. Here is a list of record breaking mean gaps which are integers:
n nth prime mean gap    2 3 0 [Honaker, May 2000] 10 29 2 " 68 337 4 " 438 3061 6 [Kok Seng Chua, May 2000] 2616 23537 8 " 100350 1304539 12 " 637198 9557957 14 " 27066970 514272413 18 " 179992840 3779849621 20 " 55762149072 1505578024919 26 [Carmody, July 2003] 382465573492 11091501631241 28 " 2636913002950 81744303091421 30 " 126979448983454 4444280714420857 34 [J. K. Andersen, April 2008] 885992692751466 32781729631804207 36 " 43525513764814972 1784546064357413813 40 " 306268030480171300 13169525310647365859 42 "   
Update: Phil Carmody has provided proof that odd mean gaps are
impossible. Note that the mean gap g occurs
about exp(g + 2).
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