
theorem
  4679 is prime
proof
  now
    4679 = 2*2339 + 1; hence not 2 divides 4679 by NAT_4:9;
    4679 = 3*1559 + 2; hence not 3 divides 4679 by NAT_4:9;
    4679 = 5*935 + 4; hence not 5 divides 4679 by NAT_4:9;
    4679 = 7*668 + 3; hence not 7 divides 4679 by NAT_4:9;
    4679 = 11*425 + 4; hence not 11 divides 4679 by NAT_4:9;
    4679 = 13*359 + 12; hence not 13 divides 4679 by NAT_4:9;
    4679 = 17*275 + 4; hence not 17 divides 4679 by NAT_4:9;
    4679 = 19*246 + 5; hence not 19 divides 4679 by NAT_4:9;
    4679 = 23*203 + 10; hence not 23 divides 4679 by NAT_4:9;
    4679 = 29*161 + 10; hence not 29 divides 4679 by NAT_4:9;
    4679 = 31*150 + 29; hence not 31 divides 4679 by NAT_4:9;
    4679 = 37*126 + 17; hence not 37 divides 4679 by NAT_4:9;
    4679 = 41*114 + 5; hence not 41 divides 4679 by NAT_4:9;
    4679 = 43*108 + 35; hence not 43 divides 4679 by NAT_4:9;
    4679 = 47*99 + 26; hence not 47 divides 4679 by NAT_4:9;
    4679 = 53*88 + 15; hence not 53 divides 4679 by NAT_4:9;
    4679 = 59*79 + 18; hence not 59 divides 4679 by NAT_4:9;
    4679 = 61*76 + 43; hence not 61 divides 4679 by NAT_4:9;
    4679 = 67*69 + 56; hence not 67 divides 4679 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4679 & n is prime
  holds not n divides 4679 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
