A066722 Numbers that can be expressed as the sum of two primes in exactly six ways.

60, 66, 72, 100, 106, 110, 116, 118, 134, 146, 166, 172, 182, 212, 248, 332

Offset: 1

Author

Peter Bertok (peter(AT)bertok.com), Jan 13 2002

Keywords

• nonn

Comments

No other terms below 10000. I conjecture there are no further terms in this sequence and A067188, A067189, etc.

R. K. Guy (Jan 14 2002) remarks: "I believe that these conjectures follow from a more general one by Hardy and Littlewood (probably in Some problems of 'partitio numerorum' III, on the expression of a number as a sum of primes, Acta Math. 44(1922) 1-70)."

Links

• Index entries for sequences related to Goldbach conjecture

Crossrefs

Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), A067187 (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), this sequence (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).

Programs

Mathematica

y = Select[Flatten@Table[Prime[i] + Prime[ j], {i, 500}, {j, 1, i}], # < Prime[500] &]; Select[Union[y], Count[y, #] == 6 &] (* Robert Price, Apr 22 2025 *)