A124013 Lesser of pair of most widely separated primes whose sum is 10^n.

3, 3, 3, 59, 11, 17, 29, 11, 71, 71, 23, 11, 29, 29, 11, 83, 3, 11, 281, 11, 101, 71, 23, 257, 401, 293, 107, 293, 53, 11, 113, 251, 47, 587, 23, 179, 389, 59, 173, 17, 1427, 83, 431, 53, 563, 593, 41, 47, 239, 383, 431, 1181, 701, 971, 149, 593, 569, 149, 191, 1973

Offset: 1

Author

Zak Seidov, Nov 02 2006

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A065577 (Number of Goldbach partitions of 10^n), A124450 (Lesser of pair of closest primes summed to 10^n).

Programs

Mathematica

Table[DeleteCases[Map[{#, 10^n - #} &, Prime@ Range@ PrimePi@ Floor[10^n/2]] /. {, k} /; ! PrimeQ@ k -> 0, 0][[1, 1]], {n, 8}] (* or *)
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 *)
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 *)

Formula

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

Extensions

a(1) corrected and a(2) inserted by Gionata Neri, Aug 01 2016