
theorem
  5501 is prime
proof
  now
    5501 = 2*2750 + 1; hence not 2 divides 5501 by NAT_4:9;
    5501 = 3*1833 + 2; hence not 3 divides 5501 by NAT_4:9;
    5501 = 5*1100 + 1; hence not 5 divides 5501 by NAT_4:9;
    5501 = 7*785 + 6; hence not 7 divides 5501 by NAT_4:9;
    5501 = 11*500 + 1; hence not 11 divides 5501 by NAT_4:9;
    5501 = 13*423 + 2; hence not 13 divides 5501 by NAT_4:9;
    5501 = 17*323 + 10; hence not 17 divides 5501 by NAT_4:9;
    5501 = 19*289 + 10; hence not 19 divides 5501 by NAT_4:9;
    5501 = 23*239 + 4; hence not 23 divides 5501 by NAT_4:9;
    5501 = 29*189 + 20; hence not 29 divides 5501 by NAT_4:9;
    5501 = 31*177 + 14; hence not 31 divides 5501 by NAT_4:9;
    5501 = 37*148 + 25; hence not 37 divides 5501 by NAT_4:9;
    5501 = 41*134 + 7; hence not 41 divides 5501 by NAT_4:9;
    5501 = 43*127 + 40; hence not 43 divides 5501 by NAT_4:9;
    5501 = 47*117 + 2; hence not 47 divides 5501 by NAT_4:9;
    5501 = 53*103 + 42; hence not 53 divides 5501 by NAT_4:9;
    5501 = 59*93 + 14; hence not 59 divides 5501 by NAT_4:9;
    5501 = 61*90 + 11; hence not 61 divides 5501 by NAT_4:9;
    5501 = 67*82 + 7; hence not 67 divides 5501 by NAT_4:9;
    5501 = 71*77 + 34; hence not 71 divides 5501 by NAT_4:9;
    5501 = 73*75 + 26; hence not 73 divides 5501 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5501 & n is prime
  holds not n divides 5501 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
