
theorem Th33:
  83 is prime
proof
  now
    let n be Element of NAT;
    83 = 2*41 + 1;
    then
A1: not 2 divides 83 by Th9;
    83 = 3*27 + 2;
    then
A2: not 3 divides 83 by Th9;
    83 = 13*6 + 5;
    then
A3: not 13 divides 83 by Th9;
    83 = 11*7 + 6;
    then
A4: not 11 divides 83 by Th9;
    83 = 19*4 + 7;
    then
A5: not 19 divides 83 by Th9;
    83 = 17*4 + 15;
    then
A6: not 17 divides 83 by Th9;
    83 = 23*3 + 14;
    then
A7: not 23 divides 83 by Th9;
    83 = 7*11 + 6;
    then
A8: not 7 divides 83 by Th9;
    83 = 5*16 + 3;
    then
A9: not 5 divides 83 by Th9;
    assume 1<n & n*n<=83 & n is prime;
    hence not n divides 83 by A1,A2,A9,A8,A4,A3,A6,A5,A7,Lm6;
  end;
  hence thesis by Th14;
end;
