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