A080854 Numbers which can be expressed as the sum of two distinct primes in exactly five ways.

48, 54, 64, 70, 76, 104, 106, 118, 124, 134, 136, 146, 148, 164, 166, 188

Offset: 1

Author

Shyam Sunder Gupta, Mar 29 2003

Keywords

• nonn

Comments

Apparently there are no further terms beyond 188. - R. J. Mathar, Oct 01 2021

Examples

			54 is a term as 54 = 31 + 23 = 37 + 17 = 41 + 13 = 43 + 11 = 47 + 7 are only the five ways to express 54 as a sum of two distinct primes.
		

Crossrefs

Cf. A077914 (2 ways), A077969 (3 ways), A078299 (4 ways), A080862 (6 ways).

Programs

Mathematica

Select[Range[200],Count[IntegerPartitions[#,{2}],?(AllTrue[#,PrimeQ]&&#[[1]]!=#[[2]]&)]==5&] (* _Harvey P. Dale, Jul 14 2025 *)

Formula

{j: A117929(j) = 5} . - R. J. Mathar, Oct 01 2021