
theorem
  7219 is prime
proof
  now
    7219 = 2*3609 + 1; hence not 2 divides 7219 by NAT_4:9;
    7219 = 3*2406 + 1; hence not 3 divides 7219 by NAT_4:9;
    7219 = 5*1443 + 4; hence not 5 divides 7219 by NAT_4:9;
    7219 = 7*1031 + 2; hence not 7 divides 7219 by NAT_4:9;
    7219 = 11*656 + 3; hence not 11 divides 7219 by NAT_4:9;
    7219 = 13*555 + 4; hence not 13 divides 7219 by NAT_4:9;
    7219 = 17*424 + 11; hence not 17 divides 7219 by NAT_4:9;
    7219 = 19*379 + 18; hence not 19 divides 7219 by NAT_4:9;
    7219 = 23*313 + 20; hence not 23 divides 7219 by NAT_4:9;
    7219 = 29*248 + 27; hence not 29 divides 7219 by NAT_4:9;
    7219 = 31*232 + 27; hence not 31 divides 7219 by NAT_4:9;
    7219 = 37*195 + 4; hence not 37 divides 7219 by NAT_4:9;
    7219 = 41*176 + 3; hence not 41 divides 7219 by NAT_4:9;
    7219 = 43*167 + 38; hence not 43 divides 7219 by NAT_4:9;
    7219 = 47*153 + 28; hence not 47 divides 7219 by NAT_4:9;
    7219 = 53*136 + 11; hence not 53 divides 7219 by NAT_4:9;
    7219 = 59*122 + 21; hence not 59 divides 7219 by NAT_4:9;
    7219 = 61*118 + 21; hence not 61 divides 7219 by NAT_4:9;
    7219 = 67*107 + 50; hence not 67 divides 7219 by NAT_4:9;
    7219 = 71*101 + 48; hence not 71 divides 7219 by NAT_4:9;
    7219 = 73*98 + 65; hence not 73 divides 7219 by NAT_4:9;
    7219 = 79*91 + 30; hence not 79 divides 7219 by NAT_4:9;
    7219 = 83*86 + 81; hence not 83 divides 7219 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7219 & n is prime
  holds not n divides 7219 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
