A152052 Number of cousin primes < 10^n.

2, 9, 41, 203, 1216, 8144, 58622, 440258, 3424680, 27409999, 224373161, 1870585459, 15834656003, 135779962760, 1177207270204

Offset: 1

Author

Cino Hilliard, Nov 22 2008

Keywords

• nonn
• hard
• more

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 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.

Examples

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

Links

• Cino Hilliard, Gcc Sum Cousin primes [broken link]

Crossrefs

Variant of A080840. [R. J. Mathar, Nov 27 2008]

Cf. A152127, A333587.

Formula

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

Extensions

a(13)-a(15) from Martin Ehrenstein, Sep 03 2021