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

1,1

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.

Links

Table of n, a(n) for n=1..18.

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

Cf. A025018, A025019.

Sequence in context: A183461 A095662 A090698 * A215802 A202041 A245507

Adjacent sequences: A350710 A350711 A350712 * A350714 A350715 A350716

Keyword

nonn,more

Author

Barry Cherkas, Feb 02 2022

Extensions

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

Status

approved