reserve n,k,b for Nat, i for Integer;

theorem Th23:
  29 is prime
  proof
    now
      let n be Element of NAT;
      29 = 2*14 + 1;
      then
      A1: not 2 divides 29 by NAT_4:9;
      29 = 3*9 + 2;
      then
      A2: not 3 divides 29 by NAT_4:9;
      29 = 5*5 + 4;
      then
      A3: not 5 divides 29 by NAT_4:9;
      29 = 7*4 + 1;
      then
      A4: not 7 divides 29 by NAT_4:9;
      29 = 11*2 + 7;
      then
      A5: not 11 divides 29 by NAT_4:9;
      29 = 13*2 + 3;
      then
      A6: not 13 divides 29 by NAT_4:9;
      29 = 17*1 + 12;
      then
      A7: not 17 divides 29 by NAT_4:9;
      29 = 19*1 + 10;
      then
      A8: not 19 divides 29 by NAT_4:9;
      29 = 23*1 + 6;
      then
      A9: not 23 divides 29 by NAT_4:9;
      assume 1<n & n*n<=29 & n is prime;
      hence not n divides 29 by A1,A2,A9,A8,A4,A3,A6,A5,A7,NAT_4:62;
    end;
    hence thesis by NAT_4:14;
  end;
