A350713 Maximum smallest prime required to generate all Goldbach partitions to 10^n.

3, 19, 73, 173, 293, 523, 751, 1093, 1789, 1877, 2803, 3457, 3917, 4909, 5569, 6961, 7753, 9341

Offset: 1

Author

Barry Cherkas, Feb 02 2022

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

Cf. A025018, A025019.

Programs

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 *)

Extensions

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