A152127 -id:A152127 - cp's OEIS frontend

A152052 Number of cousin primes < 10^n.

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

Offset: 1

Cino Hilliard, Nov 22 2008

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.

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

Cino Hilliard, Gcc Sum Cousin primes [broken link]

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

Cf. A152127, A333587.

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

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

A080840 Number of cousin primes < 10^n.

Original entry on oeis.org

1, 8, 41, 203, 1216, 8144, 58622, 440258, 3424680, 27409999, 224373161, 1870585459, 15834656003, 135779962760, 1177207270204

Offset: 1

Jason Earls, Mar 28 2003

The corresponding numbers for twin primes and sexy primes are in A007508 and A080841, the greater of twin primes, cousin primes and sexy primes are in A006512, A046132 and A046117 respectively.

In this sequence, only the upper member of each prime cousin pair is counted. See A152052 for the variant where only the lower member is counted. - James Rayman, Jan 17 2021

A. Granville and G. Martin, Prime number races, Amer. Math. Monthly vol 113, no 1 (2006) p 1.
Eric Weisstein's World of Mathematics, Cousin Primes.

Cf. A007508, A080841, A006512, A046132, A046117, A152052, A152127.

{c=0; p=5; for(n=1,9, while(p<10^n,if(isprime(p-4),c++); p=nextprime(p+1)); print1(c,","))}

a(8) and a(9) from Klaus Brockhaus, Mar 30 2003
More terms from R. J. Mathar, Aug 05 2007
a(13)-a(15) from Martin Ehrenstein, Sep 03 2021

cp's OEIS Frontend

A152052 Number of cousin primes < 10^n.

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