
theorem
  5531 is prime
proof
  now
    5531 = 2*2765 + 1; hence not 2 divides 5531 by NAT_4:9;
    5531 = 3*1843 + 2; hence not 3 divides 5531 by NAT_4:9;
    5531 = 5*1106 + 1; hence not 5 divides 5531 by NAT_4:9;
    5531 = 7*790 + 1; hence not 7 divides 5531 by NAT_4:9;
    5531 = 11*502 + 9; hence not 11 divides 5531 by NAT_4:9;
    5531 = 13*425 + 6; hence not 13 divides 5531 by NAT_4:9;
    5531 = 17*325 + 6; hence not 17 divides 5531 by NAT_4:9;
    5531 = 19*291 + 2; hence not 19 divides 5531 by NAT_4:9;
    5531 = 23*240 + 11; hence not 23 divides 5531 by NAT_4:9;
    5531 = 29*190 + 21; hence not 29 divides 5531 by NAT_4:9;
    5531 = 31*178 + 13; hence not 31 divides 5531 by NAT_4:9;
    5531 = 37*149 + 18; hence not 37 divides 5531 by NAT_4:9;
    5531 = 41*134 + 37; hence not 41 divides 5531 by NAT_4:9;
    5531 = 43*128 + 27; hence not 43 divides 5531 by NAT_4:9;
    5531 = 47*117 + 32; hence not 47 divides 5531 by NAT_4:9;
    5531 = 53*104 + 19; hence not 53 divides 5531 by NAT_4:9;
    5531 = 59*93 + 44; hence not 59 divides 5531 by NAT_4:9;
    5531 = 61*90 + 41; hence not 61 divides 5531 by NAT_4:9;
    5531 = 67*82 + 37; hence not 67 divides 5531 by NAT_4:9;
    5531 = 71*77 + 64; hence not 71 divides 5531 by NAT_4:9;
    5531 = 73*75 + 56; hence not 73 divides 5531 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5531 & n is prime
  holds not n divides 5531 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
