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A023200 Primes p such that p + 4 is also prime. 115
3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Smaller member p of cousin prime pairs (p, p+4).

A015913 contains the composite number 305635357, so it is different from both the present sequence and A029710. (305635357 is the only composite member of A015913 < 10^9.) - Jud McCranie, Jan 07 2001

Apart from the first term, all terms are of the form 6n+1.

Complement of A067775 (primes p such that p + 4 is composite) with respect to A000040 (primes). With prime 2 also primes p such that q^2 + p is prime for some prime q (q = 3 if p = 2, q = 2 if p > 2). Subsequence of A232012. - Jaroslav Krizek, Nov 23 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

A. Granville and G. Martin, Prime number races

H. J. Weber, A Sieve for Cousin Primes, arXiv:1204.3795v1 [math.NT], Apr 17, 2012.

Eric Weisstein's World of Mathematics, Cousin Primes

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for primes, gaps between

FORMULA

a(n) = A046132(n) - 4 = A087679(n) - 2.

MAPLE

A023200 := proc(n) option remember; if n = 1 then 3; else p := nextprime(procname(n-1)) ; while not isprime(p+4) do p := nextprime(p) ;  end do: p ; end if; end proc: # R. J. Mathar, Sep 03 2011

MATHEMATICA

Select[Range[10^2], PrimeQ[ # ]&&PrimeQ[ #+4] &] (Vladimir Joseph Stephan Orlovsky, Apr 29 2008)

PROG

(PARI) print1(3); p=7; forprime(q=11, 1e3, if(q-p==4, print1(", "p)); p=q) \\ Charles R Greathouse IV, Mar 20 2013

(MAGMA) [p: p in PrimesUpTo(1500) | NextPrime(p)-p eq 4]; // Bruno Berselli, Apr 09 2013

(Haskell)

a023200 n = a023200_list !! (n-1)

a023200_list = filter ((== 1) . a010051') $

               map (subtract 4) $ drop 2 a000040_list

-- Reinhard Zumkeller, Aug 01 2014

CROSSREFS

Essentially the same as A029710.

Cf. A000010, A003557, A007947, A046132, A098429.

Cf. A000040, A010051.

Sequence in context: A216518 A154650 A015913 * A046136 A098044 A217035

Adjacent sequences:  A023197 A023198 A023199 * A023201 A023202 A023203

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Definition revised by N. J. A. Sloane, Mar 05 2010

Definition modified by Vincenzo Librandi, Aug 02 2009

STATUS

approved

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Last modified November 22 23:24 EST 2014. Contains 249835 sequences.