A224534 Prime 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

Author

T. D. Noe, Apr 15 2013

Keywords

• nonn

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

Examples

			19 = 3 + 5 + 11.
		

Links

• H. A. Helfgott and David J. Platt, Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30, arXiv:1305.3062 [math.NT], 2013-2014.
• H. A. Helfgott and 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

Crossrefs

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

Programs

Mathematica

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