OFFSET

1,1

COMMENTS

The magnitude of the smallest prime required in a Goldbach partition of 2n is very small in comparison to the magnitude of the sum, 2n.

EXAMPLE

The first three partitions with the smallest first member are (3,3), (3,5), and (3,7), so the smallest prime required to generate all Goldbach partitions up through 10^1 is 3.

MATHEMATICA

gp = Compile[{{n, _Integer}}, Block[{p = 2}, While[! PrimeQ[n - p], p = NextPrime@p]; p]]; a[n] = 3; a[n_] := Block[{k = 10^(n - 1), lmt = 10^n + 1, mx = 0}, While[k < lmt, b = gp@k; If[b > mx, mx = b]; k += 2]; mx]; (* Robert G. Wilson v, Mar 04 2022 *)

CROSSREFS

KEYWORD

nonn,more

AUTHOR

Barry Cherkas, Feb 02 2022

EXTENSIONS

a(9)-a(18) from Robert G. Wilson v, Mar 04 2022

STATUS

approved