
theorem
  761 is prime
proof
  now
    761 = 2*380 + 1; hence not 2 divides 761 by NAT_4:9;
    761 = 3*253 + 2; hence not 3 divides 761 by NAT_4:9;
    761 = 5*152 + 1; hence not 5 divides 761 by NAT_4:9;
    761 = 7*108 + 5; hence not 7 divides 761 by NAT_4:9;
    761 = 11*69 + 2; hence not 11 divides 761 by NAT_4:9;
    761 = 13*58 + 7; hence not 13 divides 761 by NAT_4:9;
    761 = 17*44 + 13; hence not 17 divides 761 by NAT_4:9;
    761 = 19*40 + 1; hence not 19 divides 761 by NAT_4:9;
    761 = 23*33 + 2; hence not 23 divides 761 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 761 & n is prime
  holds not n divides 761 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
