
theorem
  5153 is prime
proof
  now
    5153 = 2*2576 + 1; hence not 2 divides 5153 by NAT_4:9;
    5153 = 3*1717 + 2; hence not 3 divides 5153 by NAT_4:9;
    5153 = 5*1030 + 3; hence not 5 divides 5153 by NAT_4:9;
    5153 = 7*736 + 1; hence not 7 divides 5153 by NAT_4:9;
    5153 = 11*468 + 5; hence not 11 divides 5153 by NAT_4:9;
    5153 = 13*396 + 5; hence not 13 divides 5153 by NAT_4:9;
    5153 = 17*303 + 2; hence not 17 divides 5153 by NAT_4:9;
    5153 = 19*271 + 4; hence not 19 divides 5153 by NAT_4:9;
    5153 = 23*224 + 1; hence not 23 divides 5153 by NAT_4:9;
    5153 = 29*177 + 20; hence not 29 divides 5153 by NAT_4:9;
    5153 = 31*166 + 7; hence not 31 divides 5153 by NAT_4:9;
    5153 = 37*139 + 10; hence not 37 divides 5153 by NAT_4:9;
    5153 = 41*125 + 28; hence not 41 divides 5153 by NAT_4:9;
    5153 = 43*119 + 36; hence not 43 divides 5153 by NAT_4:9;
    5153 = 47*109 + 30; hence not 47 divides 5153 by NAT_4:9;
    5153 = 53*97 + 12; hence not 53 divides 5153 by NAT_4:9;
    5153 = 59*87 + 20; hence not 59 divides 5153 by NAT_4:9;
    5153 = 61*84 + 29; hence not 61 divides 5153 by NAT_4:9;
    5153 = 67*76 + 61; hence not 67 divides 5153 by NAT_4:9;
    5153 = 71*72 + 41; hence not 71 divides 5153 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5153 & n is prime
  holds not n divides 5153 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
