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

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`%I #24 Mar 07 2022 02:13:15
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`%S 3,19,73,173,293,523,751,1093,1789,1877,2803,3457,3917,4909,5569,6961,
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`%T 7753,9341
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`%N Maximum smallest prime required to generate all Goldbach partitions to 10^n.
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`%C 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.
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`%e 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.
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`%t 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 *)
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`%Y Cf. A025018, A025019.
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`%K nonn,more
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`%O 1,1
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`%A _Barry Cherkas_, Feb 02 2022
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`%E a(9)-a(18) from _Robert G. Wilson v_, Mar 04 2022
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