
theorem
  751 is prime
proof
  now
    751 = 2*375 + 1; hence not 2 divides 751 by NAT_4:9;
    751 = 3*250 + 1; hence not 3 divides 751 by NAT_4:9;
    751 = 5*150 + 1; hence not 5 divides 751 by NAT_4:9;
    751 = 7*107 + 2; hence not 7 divides 751 by NAT_4:9;
    751 = 11*68 + 3; hence not 11 divides 751 by NAT_4:9;
    751 = 13*57 + 10; hence not 13 divides 751 by NAT_4:9;
    751 = 17*44 + 3; hence not 17 divides 751 by NAT_4:9;
    751 = 19*39 + 10; hence not 19 divides 751 by NAT_4:9;
    751 = 23*32 + 15; hence not 23 divides 751 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 751 & n is prime
  holds not n divides 751 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
