reserve a,b,c,k,m,n for Nat;
reserve p for Prime;

theorem
  53 satisfies_Sierpinski_problem_76b
  proof
    let x be Nat;
    assume 10*53 < x < 10*(53+1);
    then 530 < x < 539+1;
    then 530+1 <= x <= 539 by NAT_1:13;
    then x = 531 or ... or x = 539;
    hence thesis by XPRIMES0:531,532,533,534,535,536,537,538,539;
  end;
