A014091 Numbers that are the sum of 2 primes.

4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 58, 60, 61, 62, 63, 64, 66, 68, 69, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 94, 96, 98

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Sequence consists of all primes + 2 and, conjecturally (Goldbach), of all even integers larger than 2. The Goldbach conjecture is that every even number is the sum of two primes. - Emeric Deutsch, Jul 14 2004

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• David Eisenbud and Brady Haran, Goldbach Conjecture, Numberphile video (2017)
• T. Estermann, Proof that every large integer is the sum of two primes and a square, Proc. Lond. Math. Soc. 42 (1937) 501-516.

Crossrefs

Complement = A014092.

Cf. A010051, A000040, A157931 (semiprimes).

Programs

Haskell

a014091 n = a014091_list !! (n-1)
a014091_list = filter (\x -> any ((== 1) . a010051) $
                      map (x -) $ takeWhile (< x) a000040_list) [1..]
-- Reinhard Zumkeller, Oct 15 2014

Maple

sort({seq(2+ithprime(j),j=1..21)} union {seq(2*k,k=2..ceil(ithprime(21)/2))}); # Emeric Deutsch, Jul 14 2004

Mathematica

Take[ Union@ Flatten@ Table[ Prime@p + Prime@q, {p, 25}, {q, p}], 71] (* Robert G. Wilson v, Aug 31 2008 *)

PARI

isA014091(n)= my(i,p); i=1; p=prime(i); while(pA014091(a), print(n," ",a); n++)) \\ R. J. Mathar, Aug 20 2006

PARI

is(n)=if(n%2,isprime(n-2),n>2) \\ on Goldbach's conjecture; Charles R Greathouse IV, Oct 22 2013

Extensions

More terms from Robert G. Wilson v, Aug 31 2008