
theorem
  4703 is prime
proof
  now
    4703 = 2*2351 + 1; hence not 2 divides 4703 by NAT_4:9;
    4703 = 3*1567 + 2; hence not 3 divides 4703 by NAT_4:9;
    4703 = 5*940 + 3; hence not 5 divides 4703 by NAT_4:9;
    4703 = 7*671 + 6; hence not 7 divides 4703 by NAT_4:9;
    4703 = 11*427 + 6; hence not 11 divides 4703 by NAT_4:9;
    4703 = 13*361 + 10; hence not 13 divides 4703 by NAT_4:9;
    4703 = 17*276 + 11; hence not 17 divides 4703 by NAT_4:9;
    4703 = 19*247 + 10; hence not 19 divides 4703 by NAT_4:9;
    4703 = 23*204 + 11; hence not 23 divides 4703 by NAT_4:9;
    4703 = 29*162 + 5; hence not 29 divides 4703 by NAT_4:9;
    4703 = 31*151 + 22; hence not 31 divides 4703 by NAT_4:9;
    4703 = 37*127 + 4; hence not 37 divides 4703 by NAT_4:9;
    4703 = 41*114 + 29; hence not 41 divides 4703 by NAT_4:9;
    4703 = 43*109 + 16; hence not 43 divides 4703 by NAT_4:9;
    4703 = 47*100 + 3; hence not 47 divides 4703 by NAT_4:9;
    4703 = 53*88 + 39; hence not 53 divides 4703 by NAT_4:9;
    4703 = 59*79 + 42; hence not 59 divides 4703 by NAT_4:9;
    4703 = 61*77 + 6; hence not 61 divides 4703 by NAT_4:9;
    4703 = 67*70 + 13; hence not 67 divides 4703 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4703 & n is prime
  holds not n divides 4703 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
