A080840 Number of cousin primes < 10^n.

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

Offset: 1

Author

Jason Earls, Mar 28 2003

Keywords

• nonn
• hard
• more

Comments

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

Links

• 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.

Crossrefs

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

Programs

PARI

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

Extensions

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