
theorem
  5527 is prime
proof
  now
    5527 = 2*2763 + 1; hence not 2 divides 5527 by NAT_4:9;
    5527 = 3*1842 + 1; hence not 3 divides 5527 by NAT_4:9;
    5527 = 5*1105 + 2; hence not 5 divides 5527 by NAT_4:9;
    5527 = 7*789 + 4; hence not 7 divides 5527 by NAT_4:9;
    5527 = 11*502 + 5; hence not 11 divides 5527 by NAT_4:9;
    5527 = 13*425 + 2; hence not 13 divides 5527 by NAT_4:9;
    5527 = 17*325 + 2; hence not 17 divides 5527 by NAT_4:9;
    5527 = 19*290 + 17; hence not 19 divides 5527 by NAT_4:9;
    5527 = 23*240 + 7; hence not 23 divides 5527 by NAT_4:9;
    5527 = 29*190 + 17; hence not 29 divides 5527 by NAT_4:9;
    5527 = 31*178 + 9; hence not 31 divides 5527 by NAT_4:9;
    5527 = 37*149 + 14; hence not 37 divides 5527 by NAT_4:9;
    5527 = 41*134 + 33; hence not 41 divides 5527 by NAT_4:9;
    5527 = 43*128 + 23; hence not 43 divides 5527 by NAT_4:9;
    5527 = 47*117 + 28; hence not 47 divides 5527 by NAT_4:9;
    5527 = 53*104 + 15; hence not 53 divides 5527 by NAT_4:9;
    5527 = 59*93 + 40; hence not 59 divides 5527 by NAT_4:9;
    5527 = 61*90 + 37; hence not 61 divides 5527 by NAT_4:9;
    5527 = 67*82 + 33; hence not 67 divides 5527 by NAT_4:9;
    5527 = 71*77 + 60; hence not 71 divides 5527 by NAT_4:9;
    5527 = 73*75 + 52; hence not 73 divides 5527 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5527 & n is prime
  holds not n divides 5527 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
