

A152052


Number of cousin primes < 10^n.


4



2, 9, 41, 203, 1216, 8144, 58622, 440258, 3424680, 27409999, 224373161, 1870585459, 15834656003, 135779962760, 1177207270204
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The convention here is that only the lower member of a cousin prime pair be less than the selected bound 10^n.
Cousin primes, like twin primes, can be approximated by the HardyLittlewood formula for the number of twin primes < n. For example, the number of cousin primes < 10^12 = 1870585459 while HardyLittlewood 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.


LINKS



FORMULA

A cousin prime pair is a pair of primes that differ by 4.


EXAMPLE

(3,7) and (7,11) are cousin primes < 10 since 7 < 10. So 2 is the first entry in the sequence.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



