
theorem
  2131 is prime
proof
  now
    2131 = 2*1065 + 1; hence not 2 divides 2131 by NAT_4:9;
    2131 = 3*710 + 1; hence not 3 divides 2131 by NAT_4:9;
    2131 = 5*426 + 1; hence not 5 divides 2131 by NAT_4:9;
    2131 = 7*304 + 3; hence not 7 divides 2131 by NAT_4:9;
    2131 = 11*193 + 8; hence not 11 divides 2131 by NAT_4:9;
    2131 = 13*163 + 12; hence not 13 divides 2131 by NAT_4:9;
    2131 = 17*125 + 6; hence not 17 divides 2131 by NAT_4:9;
    2131 = 19*112 + 3; hence not 19 divides 2131 by NAT_4:9;
    2131 = 23*92 + 15; hence not 23 divides 2131 by NAT_4:9;
    2131 = 29*73 + 14; hence not 29 divides 2131 by NAT_4:9;
    2131 = 31*68 + 23; hence not 31 divides 2131 by NAT_4:9;
    2131 = 37*57 + 22; hence not 37 divides 2131 by NAT_4:9;
    2131 = 41*51 + 40; hence not 41 divides 2131 by NAT_4:9;
    2131 = 43*49 + 24; hence not 43 divides 2131 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2131 & n is prime
  holds not n divides 2131 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
