
theorem
  4919 is prime
proof
  now
    4919 = 2*2459 + 1; hence not 2 divides 4919 by NAT_4:9;
    4919 = 3*1639 + 2; hence not 3 divides 4919 by NAT_4:9;
    4919 = 5*983 + 4; hence not 5 divides 4919 by NAT_4:9;
    4919 = 7*702 + 5; hence not 7 divides 4919 by NAT_4:9;
    4919 = 11*447 + 2; hence not 11 divides 4919 by NAT_4:9;
    4919 = 13*378 + 5; hence not 13 divides 4919 by NAT_4:9;
    4919 = 17*289 + 6; hence not 17 divides 4919 by NAT_4:9;
    4919 = 19*258 + 17; hence not 19 divides 4919 by NAT_4:9;
    4919 = 23*213 + 20; hence not 23 divides 4919 by NAT_4:9;
    4919 = 29*169 + 18; hence not 29 divides 4919 by NAT_4:9;
    4919 = 31*158 + 21; hence not 31 divides 4919 by NAT_4:9;
    4919 = 37*132 + 35; hence not 37 divides 4919 by NAT_4:9;
    4919 = 41*119 + 40; hence not 41 divides 4919 by NAT_4:9;
    4919 = 43*114 + 17; hence not 43 divides 4919 by NAT_4:9;
    4919 = 47*104 + 31; hence not 47 divides 4919 by NAT_4:9;
    4919 = 53*92 + 43; hence not 53 divides 4919 by NAT_4:9;
    4919 = 59*83 + 22; hence not 59 divides 4919 by NAT_4:9;
    4919 = 61*80 + 39; hence not 61 divides 4919 by NAT_4:9;
    4919 = 67*73 + 28; hence not 67 divides 4919 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4919 & n is prime
  holds not n divides 4919 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
