A224534 Primes numbers that are the sum of three distinct prime numbers.

19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset

1,1

Comments

Similar to Goldbach's weak conjecture.

Primes in A124867, and by the comment in A124867 also the set of all primes >=19. - R. J. Mathar, Apr 19 2013

"Goldbach's original conjecture (sometimes called the 'ternary' Goldbach conjecture), written in a June 7, 1742 letter to Euler, states 'at least it seems that every number that is greater than 2 is the sum of three primes' (Goldbach 1742; Dickson 2005, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed." [Weisstein] - Jonathan Vos Post, May 15 2013

Links

Table of n, a(n) for n=1..56.

H. A. Helfgott, David J. Platt, Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30, arXiv:1305.3062v1 [math.NT], May 14, 2013.

H. A. Helfgott, David J. Platt, Numerical verification of the Ternary Goldbach Conjecture up to 8.875*10^30, Exp. Math. 22 (4) (2013) 406-409.

Eric W. Weisstein, Goldbach conjecture

Wikipedia, Goldbach's conjecture

Wikipedia, Goldbach's weak conjecture

Example

19 = 3 + 5 + 11.

Mathematica

Union[Select[Total /@ Subsets[Prime[Range[2, 30]], {3}], PrimeQ]]

Crossrefs

Cf. A002372, A002375, A024684 (number of sums), A224535, A166063, A166061, A071621.

Sequence in context: A159021 A100460 A166061 * A073319 A274048 A334093

Adjacent sequences: A224531 A224532 A224533 * A224535 A224536 A224537

Keyword

nonn

Author

T. D. Noe, Apr 15 2013

Status

approved