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%I #18 Feb 26 2024 01:57:04
%S 3,3,3,59,11,17,29,11,71,71,23,11,29,29,11,83,3,11,281,11,101,71,23,
%T 257,401,293,107,293,53,11,113,251,47,587,23,179,389,59,173,17,1427,
%U 83,431,53,563,593,41,47,239,383,431,1181,701,971,149,593,569,149,191,1973
%N Lesser of pair of most widely separated primes whose sum is 10^n.
%F 10^n - a(n) is prime and 10^n - k is composite for 0 <= k < a(n). - corrected by _David A. Corneth_, Aug 18 2016
%e 10^1 = 3 + 7, 10^2 = 3 + 97, 10^3 = 3 + 997, 10^4 = 59 + 9941, 10^5 = 11 + 99989, 10^6 = 17 + 999983, 10^7 = 29 + 9999971, 10^8 = 11 + 99999989, 10^9 = 71 + 999999929, 10^10 = 71 + 9999999929, etc.
%t Table[DeleteCases[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]] /. {_, k_} /; ! PrimeQ@ k -> 0, 0][[1, 1]], {n, 8}] (* or *)
%t Table[First@ SelectFirst[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]], PrimeQ@ Last@ # &], {n, 9}] (* Version 10, _Michael De Vlieger_, Aug 01 2016 *)
%t lp[n_]:=Module[{p=3,x=10^n},While[CompositeQ[x-p],p=NextPrime[p]];p]; Array[lp,60] (* _Harvey P. Dale_, Jun 11 2022 *)
%Y Cf. A065577 (Number of Goldbach partitions of 10^n), A124450 (Lesser of pair of closest primes summed to 10^n).
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 02 2006
%E a(1) corrected and a(2) inserted by _Gionata Neri_, Aug 01 2016
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