cp's OEIS Frontend

A014091 Numbers that are the sum of 2 primes.

%I A014091 #31 Jul 08 2025 02:52:26
%S A014091 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,
%T A014091 34,36,38,39,40,42,43,44,45,46,48,49,50,52,54,55,56,58,60,61,62,63,64,
%U A014091 66,68,69,70,72,73,74,75,76,78,80,81,82,84,85,86,88,90,91,92,94,96,98
%N A014091 Numbers that are the sum of 2 primes.
%C A014091 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
%H A014091 T. D. Noe, <a href="/A014091/b014091.txt">Table of n, a(n) for n = 1..1000</a>
%H A014091 David Eisenbud and Brady Haran, <a href="https://www.youtube.com/watch?v=MxiTG96QOxw">Goldbach Conjecture</a>, Numberphile video (2017)
%H A014091 T. Estermann, <a href="http://dx.doi.org/10.1112/plms/s2-42.1.501">Proof that every large integer is the sum of two primes and a square</a>, Proc. Lond. Math. Soc. 42 (1937) 501-516.
%p A014091 sort({seq(2+ithprime(j),j=1..21)} union {seq(2*k,k=2..ceil(ithprime(21)/2))}); # _Emeric Deutsch_, Jul 14 2004
%t A014091 Take[ Union@ Flatten@ Table[ Prime@p + Prime@q, {p, 25}, {q, p}], 71] (* _Robert G. Wilson v_, Aug 31 2008 *)
%o A014091 (PARI) isA014091(n)= my(i,p); i=1; p=prime(i); while(p<n, if( isprime(n-p), return(1)); i++; p=prime(i)); 0
%o A014091 n=0; for(a=2,100, if(isA014091(a), print(n," ",a); n++)) \\ _R. J. Mathar_, Aug 20 2006
%o A014091 (PARI) is(n)=if(n%2,isprime(n-2),n>2) \\ on Goldbach's conjecture; _Charles R Greathouse IV_, Oct 22 2013
%o A014091 (Haskell)
%o A014091 a014091 n = a014091_list !! (n-1)
%o A014091 a014091_list = filter (\x -> any ((== 1) . a010051) $
%o A014091                       map (x -) $ takeWhile (< x) a000040_list) [1..]
%o A014091 -- _Reinhard Zumkeller_, Oct 15 2014
%Y A014091 Complement = A014092.
%Y A014091 Cf. A010051, A000040,  A157931 (semiprimes).
%K A014091 nonn
%O A014091 1,1
%A A014091 _N. J. A. Sloane_
%E A014091 More terms from _Robert G. Wilson v_, Aug 31 2008