

A152052


Number of cousin primes < 10^n.


3



2, 9, 41, 203, 1216, 8144, 58622, 440258, 3424680, 27409999, 224373161, 1870585459
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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

Table of n, a(n) for n=1..12.
Cino Hilliard, Gcc Sum Cousin primes [broken link]


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

Variant of A080840. [R. J. Mathar, Nov 27 2008]
Sequence in context: A292078 A270766 A181375 * A192661 A020038 A330016
Adjacent sequences: A152049 A152050 A152051 * A152053 A152054 A152055


KEYWORD

nonn,hard,more


AUTHOR

Cino Hilliard, Nov 22 2008


STATUS

approved



