
theorem Th34:
  139 is prime
proof
  now
    let n be Element of NAT;
    139 = 2*69 + 1;
    then
A1: not 2 divides 139 by Th9;
    139 = 3*46 + 1;
    then
A2: not 3 divides 139 by Th9;
    139 = 13*10 + 9;
    then
A3: not 13 divides 139 by Th9;
    139 = 11*12 + 7;
    then
A4: not 11 divides 139 by Th9;
    139 = 19*7 + 6;
    then
A5: not 19 divides 139 by Th9;
    139 = 17*8 + 3;
    then
A6: not 17 divides 139 by Th9;
    139 = 23*6 + 1;
    then
A7: not 23 divides 139 by Th9;
    139 = 7*19 + 6;
    then
A8: not 7 divides 139 by Th9;
    139 = 5*27 + 4;
    then
A9: not 5 divides 139 by Th9;
    assume 1<n & n*n<=139 & n is prime;
    hence not n divides 139 by A1,A2,A9,A8,A4,A3,A6,A5,A7,Lm6;
  end;
  hence thesis by Th14;
end;
