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

theorem Th25:
  41 is prime
  proof
    now
      let n be Element of NAT;
      41 = 2*20 + 1;
      then
      A1: not 2 divides 41 by NAT_4:9;
      41 = 3*13 + 2;
      then
      A2: not 3 divides 41 by NAT_4:9;
      41 = 5*8 + 1;
      then
      A3: not 5 divides 41 by NAT_4:9;
      41 = 7*5 + 6;
      then
      A4: not 7 divides 41 by NAT_4:9;
      41 = 11*3 + 8;
      then
      A5: not 11 divides 41 by NAT_4:9;
      41 = 13*3 + 2;
      then
      A6: not 13 divides 41 by NAT_4:9;
      41 = 17*2 + 7;
      then
      A7: not 17 divides 41 by NAT_4:9;
      41 = 19*2 + 3;
      then
      A8: not 19 divides 41 by NAT_4:9;
      41 = 23*1 + 18;
      then
      A9: not 23 divides 41 by NAT_4:9;
      assume 1<n & n*n<=41 & n is prime;
      hence not n divides 41 by A1,A2,A3,A4,A5,A6,A7,A8,A9,NAT_4:62;
    end;
    hence thesis by NAT_4:14;
  end;
