
theorem
  1451 is prime
proof
  now
    1451 = 2*725 + 1; hence not 2 divides 1451 by NAT_4:9;
    1451 = 3*483 + 2; hence not 3 divides 1451 by NAT_4:9;
    1451 = 5*290 + 1; hence not 5 divides 1451 by NAT_4:9;
    1451 = 7*207 + 2; hence not 7 divides 1451 by NAT_4:9;
    1451 = 11*131 + 10; hence not 11 divides 1451 by NAT_4:9;
    1451 = 13*111 + 8; hence not 13 divides 1451 by NAT_4:9;
    1451 = 17*85 + 6; hence not 17 divides 1451 by NAT_4:9;
    1451 = 19*76 + 7; hence not 19 divides 1451 by NAT_4:9;
    1451 = 23*63 + 2; hence not 23 divides 1451 by NAT_4:9;
    1451 = 29*50 + 1; hence not 29 divides 1451 by NAT_4:9;
    1451 = 31*46 + 25; hence not 31 divides 1451 by NAT_4:9;
    1451 = 37*39 + 8; hence not 37 divides 1451 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1451 & n is prime
  holds not n divides 1451 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
