
theorem
  2179 is prime
proof
  now
    2179 = 2*1089 + 1; hence not 2 divides 2179 by NAT_4:9;
    2179 = 3*726 + 1; hence not 3 divides 2179 by NAT_4:9;
    2179 = 5*435 + 4; hence not 5 divides 2179 by NAT_4:9;
    2179 = 7*311 + 2; hence not 7 divides 2179 by NAT_4:9;
    2179 = 11*198 + 1; hence not 11 divides 2179 by NAT_4:9;
    2179 = 13*167 + 8; hence not 13 divides 2179 by NAT_4:9;
    2179 = 17*128 + 3; hence not 17 divides 2179 by NAT_4:9;
    2179 = 19*114 + 13; hence not 19 divides 2179 by NAT_4:9;
    2179 = 23*94 + 17; hence not 23 divides 2179 by NAT_4:9;
    2179 = 29*75 + 4; hence not 29 divides 2179 by NAT_4:9;
    2179 = 31*70 + 9; hence not 31 divides 2179 by NAT_4:9;
    2179 = 37*58 + 33; hence not 37 divides 2179 by NAT_4:9;
    2179 = 41*53 + 6; hence not 41 divides 2179 by NAT_4:9;
    2179 = 43*50 + 29; hence not 43 divides 2179 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2179 & n is prime
  holds not n divides 2179 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
