
theorem
  4139 is prime
proof
  now
    4139 = 2*2069 + 1; hence not 2 divides 4139 by NAT_4:9;
    4139 = 3*1379 + 2; hence not 3 divides 4139 by NAT_4:9;
    4139 = 5*827 + 4; hence not 5 divides 4139 by NAT_4:9;
    4139 = 7*591 + 2; hence not 7 divides 4139 by NAT_4:9;
    4139 = 11*376 + 3; hence not 11 divides 4139 by NAT_4:9;
    4139 = 13*318 + 5; hence not 13 divides 4139 by NAT_4:9;
    4139 = 17*243 + 8; hence not 17 divides 4139 by NAT_4:9;
    4139 = 19*217 + 16; hence not 19 divides 4139 by NAT_4:9;
    4139 = 23*179 + 22; hence not 23 divides 4139 by NAT_4:9;
    4139 = 29*142 + 21; hence not 29 divides 4139 by NAT_4:9;
    4139 = 31*133 + 16; hence not 31 divides 4139 by NAT_4:9;
    4139 = 37*111 + 32; hence not 37 divides 4139 by NAT_4:9;
    4139 = 41*100 + 39; hence not 41 divides 4139 by NAT_4:9;
    4139 = 43*96 + 11; hence not 43 divides 4139 by NAT_4:9;
    4139 = 47*88 + 3; hence not 47 divides 4139 by NAT_4:9;
    4139 = 53*78 + 5; hence not 53 divides 4139 by NAT_4:9;
    4139 = 59*70 + 9; hence not 59 divides 4139 by NAT_4:9;
    4139 = 61*67 + 52; hence not 61 divides 4139 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4139 & n is prime
  holds not n divides 4139 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
