OFFSET
1,1
COMMENTS
There are no other terms below 10000 and I conjecture there are no further terms in this sequence and A067188, A067189, etc. - Peter Bertok (peter(AT)bertok.com), Jan 13 2002
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). - R. K. Guy, Jan 14 2002
There are no further terms through 50000. - David Wasserman, Jan 15 2002
EXAMPLE
70 is a term as 70 = 67 + 3 = 59 + 11 = 53 + 17 = 47 + 23 41 + 29 are all the five ways to express 70 as a sum of two primes.
MATHEMATICA
upperbound=10^4; range=ConstantArray[0, 2*upperbound];
primeRange=Prime[Range[PrimePi[upperbound]]];
(range[[Plus@@#]]++)&/@(DeleteDuplicates[Sort[#]&/@Tuples[primeRange, 2]]); {"upperbound="<>ToString[upperbound], Flatten[Position[Take[range, upperbound], 5]]} (* Hans Rudolf Widmer, Jul 06 2021 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Jan 10 2002
EXTENSIONS
Corrected and extended by Peter Bertok (peter(AT)bertok.com), Jan 13 2002
STATUS
approved