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%I #28 Oct 08 2021 07:41:15
%S 2,9,41,203,1216,8144,58622,440258,3424680,27409999,224373161,
%T 1870585459,15834656003,135779962760,1177207270204
%N Number of cousin primes < 10^n.
%C The convention here is that only the lower member of a cousin prime pair be less than the selected bound 10^n.
%C Cousin primes, like twin primes, can be approximated by the Hardy-Littlewood formula for the number of twin primes < n. For example, the number of cousin primes < 10^12 = 1870585459 while Hardy-Littlewood gives 1870559867. The sum of cousin primes < 10^6 divided by 4 also approximates the number of cousin primes < 10^12 with 1844802199. These two methods are asymptotic to the true value as n -> infinity.
%H Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/sum-of-cousin-primes--10-n">Gcc Sum Cousin primes</a> [broken link]
%F A cousin prime pair is a pair of primes that differ by 4.
%e (3,7) and (7,11) are cousin primes < 10 since 7 < 10. So 2 is the first entry in the sequence.
%Y Variant of A080840. [_R. J. Mathar_, Nov 27 2008]
%Y Cf. A152127, A333587.
%K nonn,hard,more
%O 1,1
%A _Cino Hilliard_, Nov 22 2008
%E a(13)-a(15) from _Martin Ehrenstein_, Sep 03 2021