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%I #8 Mar 13 2022 19:14:16
%S -1,-1,68,128,152,188,332,398,368,488,632,692,626,992,878,908,1112,
%T 998,1412,1202,1448,1718,1532,1604,1682,2048,2252,2078,2672,2642,2456,
%U 2936,2504,2588,2978,3092,3032,3218,3272,3296,3632,3548,3754,4022,4058,4412,4448
%N Conjectured largest number that can be expressed as the sum of two primes in exactly n ways or -1 if no such number exists.
%C Conjecture A in page 32 of the Hardy and Littlewood reference implies that a(n) != -1 for all n > 1. While the sequence is not monotonic, the plot of n versus a(n)/log(a(n))^2 has a linear trend which matches with the formula for the number of representations in Conjecture A.
%H G. H. Hardy and J. E. Littlewood, <a href="https://doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes</a>, Acta Mathematica, volume 44, pages 1-70 (1923).
%Y Cf. A352296.
%Y Essentially the same as A000954.
%K sign
%O 0,3
%A _Chai Wah Wu_, Mar 11 2022