
theorem
  701 is prime
proof
  now
    701 = 2*350 + 1; hence not 2 divides 701 by NAT_4:9;
    701 = 3*233 + 2; hence not 3 divides 701 by NAT_4:9;
    701 = 5*140 + 1; hence not 5 divides 701 by NAT_4:9;
    701 = 7*100 + 1; hence not 7 divides 701 by NAT_4:9;
    701 = 11*63 + 8; hence not 11 divides 701 by NAT_4:9;
    701 = 13*53 + 12; hence not 13 divides 701 by NAT_4:9;
    701 = 17*41 + 4; hence not 17 divides 701 by NAT_4:9;
    701 = 19*36 + 17; hence not 19 divides 701 by NAT_4:9;
    701 = 23*30 + 11; hence not 23 divides 701 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 701 & n is prime
  holds not n divides 701 by XPRIMET1:18;
  hence thesis by NAT_4:14;
