
theorem
  757 is prime
proof
  now
    757 = 2*378 + 1; hence not 2 divides 757 by NAT_4:9;
    757 = 3*252 + 1; hence not 3 divides 757 by NAT_4:9;
    757 = 5*151 + 2; hence not 5 divides 757 by NAT_4:9;
    757 = 7*108 + 1; hence not 7 divides 757 by NAT_4:9;
    757 = 11*68 + 9; hence not 11 divides 757 by NAT_4:9;
    757 = 13*58 + 3; hence not 13 divides 757 by NAT_4:9;
    757 = 17*44 + 9; hence not 17 divides 757 by NAT_4:9;
    757 = 19*39 + 16; hence not 19 divides 757 by NAT_4:9;
    757 = 23*32 + 21; hence not 23 divides 757 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 757 & n is prime
  holds not n divides 757 by XPRIMET1:18;
  hence thesis by NAT_4:14;
