
theorem
  5521 is prime
proof
  now
    5521 = 2*2760 + 1; hence not 2 divides 5521 by NAT_4:9;
    5521 = 3*1840 + 1; hence not 3 divides 5521 by NAT_4:9;
    5521 = 5*1104 + 1; hence not 5 divides 5521 by NAT_4:9;
    5521 = 7*788 + 5; hence not 7 divides 5521 by NAT_4:9;
    5521 = 11*501 + 10; hence not 11 divides 5521 by NAT_4:9;
    5521 = 13*424 + 9; hence not 13 divides 5521 by NAT_4:9;
    5521 = 17*324 + 13; hence not 17 divides 5521 by NAT_4:9;
    5521 = 19*290 + 11; hence not 19 divides 5521 by NAT_4:9;
    5521 = 23*240 + 1; hence not 23 divides 5521 by NAT_4:9;
    5521 = 29*190 + 11; hence not 29 divides 5521 by NAT_4:9;
    5521 = 31*178 + 3; hence not 31 divides 5521 by NAT_4:9;
    5521 = 37*149 + 8; hence not 37 divides 5521 by NAT_4:9;
    5521 = 41*134 + 27; hence not 41 divides 5521 by NAT_4:9;
    5521 = 43*128 + 17; hence not 43 divides 5521 by NAT_4:9;
    5521 = 47*117 + 22; hence not 47 divides 5521 by NAT_4:9;
    5521 = 53*104 + 9; hence not 53 divides 5521 by NAT_4:9;
    5521 = 59*93 + 34; hence not 59 divides 5521 by NAT_4:9;
    5521 = 61*90 + 31; hence not 61 divides 5521 by NAT_4:9;
    5521 = 67*82 + 27; hence not 67 divides 5521 by NAT_4:9;
    5521 = 71*77 + 54; hence not 71 divides 5521 by NAT_4:9;
    5521 = 73*75 + 46; hence not 73 divides 5521 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5521 & n is prime
  holds not n divides 5521 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
