
theorem Th36:
  317 is prime
proof
  now
    let n be Element of NAT;
    317 = 2*158 + 1;
    then
A1: not 2 divides 317 by Th9;
    317 = 3*105 + 2;
    then
A2: not 3 divides 317 by Th9;
    317 = 13*24 + 5;
    then
A3: not 13 divides 317 by Th9;
    317 = 11*28 + 9;
    then
A4: not 11 divides 317 by Th9;
    317 = 19*16 + 13;
    then
A5: not 19 divides 317 by Th9;
    317 = 17*18 + 11;
    then
A6: not 17 divides 317 by Th9;
    317 = 23*13 + 18;
    then
A7: not 23 divides 317 by Th9;
    317 = 7*45 + 2;
    then
A8: not 7 divides 317 by Th9;
    317 = 5*63 + 2;
    then
A9: not 5 divides 317 by Th9;
    assume 1<n & n*n<=317 & n is prime;
    hence not n divides 317 by A1,A2,A9,A8,A4,A3,A6,A5,A7,Lm6;
  end;
  hence thesis by Th14;
end;
