
theorem
  4079 is prime
proof
  now
    4079 = 2*2039 + 1; hence not 2 divides 4079 by NAT_4:9;
    4079 = 3*1359 + 2; hence not 3 divides 4079 by NAT_4:9;
    4079 = 5*815 + 4; hence not 5 divides 4079 by NAT_4:9;
    4079 = 7*582 + 5; hence not 7 divides 4079 by NAT_4:9;
    4079 = 11*370 + 9; hence not 11 divides 4079 by NAT_4:9;
    4079 = 13*313 + 10; hence not 13 divides 4079 by NAT_4:9;
    4079 = 17*239 + 16; hence not 17 divides 4079 by NAT_4:9;
    4079 = 19*214 + 13; hence not 19 divides 4079 by NAT_4:9;
    4079 = 23*177 + 8; hence not 23 divides 4079 by NAT_4:9;
    4079 = 29*140 + 19; hence not 29 divides 4079 by NAT_4:9;
    4079 = 31*131 + 18; hence not 31 divides 4079 by NAT_4:9;
    4079 = 37*110 + 9; hence not 37 divides 4079 by NAT_4:9;
    4079 = 41*99 + 20; hence not 41 divides 4079 by NAT_4:9;
    4079 = 43*94 + 37; hence not 43 divides 4079 by NAT_4:9;
    4079 = 47*86 + 37; hence not 47 divides 4079 by NAT_4:9;
    4079 = 53*76 + 51; hence not 53 divides 4079 by NAT_4:9;
    4079 = 59*69 + 8; hence not 59 divides 4079 by NAT_4:9;
    4079 = 61*66 + 53; hence not 61 divides 4079 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4079 & n is prime
  holds not n divides 4079 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
