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A224534 Primes numbers that are the sum of three distinct prime numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)