
theorem Th35:
  163 is prime
proof
  now
    let n be Element of NAT;
    163 = 2*81 + 1;
    then
A1: not 2 divides 163 by Th9;
    163 = 3*54 + 1;
    then
A2: not 3 divides 163 by Th9;
    163 = 13*12 + 7;
    then
A3: not 13 divides 163 by Th9;
    163 = 11*14 + 9;
    then
A4: not 11 divides 163 by Th9;
    163 = 19*8 + 11;
    then
A5: not 19 divides 163 by Th9;
    163 = 17*9 + 10;
    then
A6: not 17 divides 163 by Th9;
    163 = 23*7 + 2;
    then
A7: not 23 divides 163 by Th9;
    163 = 7*23 + 2;
    then
A8: not 7 divides 163 by Th9;
    163 = 5*32 + 3;
    then
A9: not 5 divides 163 by Th9;
    assume 1<n & n*n<=163 & n is prime;
    hence not n divides 163 by A1,A2,A9,A8,A4,A3,A6,A5,A7,Lm6;
  end;
  hence thesis by Th14;
end;
