
theorem
  2551 is prime
proof
  now
    2551 = 2*1275 + 1; hence not 2 divides 2551 by NAT_4:9;
    2551 = 3*850 + 1; hence not 3 divides 2551 by NAT_4:9;
    2551 = 5*510 + 1; hence not 5 divides 2551 by NAT_4:9;
    2551 = 7*364 + 3; hence not 7 divides 2551 by NAT_4:9;
    2551 = 11*231 + 10; hence not 11 divides 2551 by NAT_4:9;
    2551 = 13*196 + 3; hence not 13 divides 2551 by NAT_4:9;
    2551 = 17*150 + 1; hence not 17 divides 2551 by NAT_4:9;
    2551 = 19*134 + 5; hence not 19 divides 2551 by NAT_4:9;
    2551 = 23*110 + 21; hence not 23 divides 2551 by NAT_4:9;
    2551 = 29*87 + 28; hence not 29 divides 2551 by NAT_4:9;
    2551 = 31*82 + 9; hence not 31 divides 2551 by NAT_4:9;
    2551 = 37*68 + 35; hence not 37 divides 2551 by NAT_4:9;
    2551 = 41*62 + 9; hence not 41 divides 2551 by NAT_4:9;
    2551 = 43*59 + 14; hence not 43 divides 2551 by NAT_4:9;
    2551 = 47*54 + 13; hence not 47 divides 2551 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2551 & n is prime
  holds not n divides 2551 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
