
theorem
  4219 is prime
proof
  now
    4219 = 2*2109 + 1; hence not 2 divides 4219 by NAT_4:9;
    4219 = 3*1406 + 1; hence not 3 divides 4219 by NAT_4:9;
    4219 = 5*843 + 4; hence not 5 divides 4219 by NAT_4:9;
    4219 = 7*602 + 5; hence not 7 divides 4219 by NAT_4:9;
    4219 = 11*383 + 6; hence not 11 divides 4219 by NAT_4:9;
    4219 = 13*324 + 7; hence not 13 divides 4219 by NAT_4:9;
    4219 = 17*248 + 3; hence not 17 divides 4219 by NAT_4:9;
    4219 = 19*222 + 1; hence not 19 divides 4219 by NAT_4:9;
    4219 = 23*183 + 10; hence not 23 divides 4219 by NAT_4:9;
    4219 = 29*145 + 14; hence not 29 divides 4219 by NAT_4:9;
    4219 = 31*136 + 3; hence not 31 divides 4219 by NAT_4:9;
    4219 = 37*114 + 1; hence not 37 divides 4219 by NAT_4:9;
    4219 = 41*102 + 37; hence not 41 divides 4219 by NAT_4:9;
    4219 = 43*98 + 5; hence not 43 divides 4219 by NAT_4:9;
    4219 = 47*89 + 36; hence not 47 divides 4219 by NAT_4:9;
    4219 = 53*79 + 32; hence not 53 divides 4219 by NAT_4:9;
    4219 = 59*71 + 30; hence not 59 divides 4219 by NAT_4:9;
    4219 = 61*69 + 10; hence not 61 divides 4219 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4219 & n is prime
  holds not n divides 4219 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
