reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i for Integer;
reserve r for Real;
reserve p for Prime;

theorem Th66:
  10|^(6*k+4) + 3 is composite
  proof
    set z = 10|^(6*k+4) + 3;
    0+2 <= z by XREAL_1:7;
    hence 2 <= z;
    0+1 < 6*k+4 by XREAL_1:8;
    then 10|^1 < 10|^(6*k+4) by PEPIN:66;
    then 10+3 < z by XREAL_1:8;
    then 7 < z by XXREAL_0:2;
    hence thesis by Th65;
  end;
