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

theorem Th30:
  3 satisfies_Sierpinski_problem_121_for 7
  proof
    set n = 3;
    thus 7 * 2|^(2|^n) + 1 is composite by Lm3,Lm6,XPRIMES0:1793;
    let m be positive Nat;
    assume m < n;
    then per cases by Th1;
    suppose m = 0;
      hence thesis;
    end;
    suppose m = 1;
      hence thesis by Lm2,XPRIMES1:29;
    end;
    suppose m = 2;
      hence thesis by Lm2,Lm4,XPRIMES1:113;
    end;
  end;
