

A023200


Primes p such that p + 4 is also prime.


117



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
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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
Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n). Namely a(n)^(1/n) is a strictly decreasing function of n.  Jahangeer Kholdi and Farideh Firoozbakht, Nov 24 2014


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(n1)) ; 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(qp==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 !! (n1)
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.
Cf. A248851, A248852, A248853.
Sequence in context: A216518 A154650 A015913 * A046136 A098044 A252091
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



