A080862 Numbers which can be expressed as the sum of two distinct primes in exactly six ways.

60, 66, 72, 100, 110, 116, 172, 178, 182, 194, 206, 212, 218, 226, 248, 278, 326, 332, 398

Offset: 1

Author

Shyam Sunder Gupta, Mar 29 2003

Keywords

• nonn
• changed

Comments

Apparently there are no further terms beyond 398. - R. J. Mathar, Oct 01 2021

Examples

			66 is a term as 66 = 37 + 29 = 43 + 23 = 47 + 17 = 53 + 13 = 59 + 7 = 61 + 5 are only the six ways to express 66 as a sum of two distinct primes.
		

Crossrefs

Cf. A077914 (2 ways), A077969 (3 ways), A078299 (4 ways), A080854 (5 ways).

Programs

Mathematica

tdpQ[n_]:=Count[IntegerPartitions[n,{2}],?(AllTrue[#,PrimeQ]&&Length[Union[#]]==2&)]==6; Select[Range[400],tdpQ] (* _Harvey P. Dale, Aug 17 2025 *)

Formula

{j: A117929(j) = 6}. - R. J. Mathar, Oct 01 2021