
theorem
  4073 is prime
proof
  now
    4073 = 2*2036 + 1; hence not 2 divides 4073 by NAT_4:9;
    4073 = 3*1357 + 2; hence not 3 divides 4073 by NAT_4:9;
    4073 = 5*814 + 3; hence not 5 divides 4073 by NAT_4:9;
    4073 = 7*581 + 6; hence not 7 divides 4073 by NAT_4:9;
    4073 = 11*370 + 3; hence not 11 divides 4073 by NAT_4:9;
    4073 = 13*313 + 4; hence not 13 divides 4073 by NAT_4:9;
    4073 = 17*239 + 10; hence not 17 divides 4073 by NAT_4:9;
    4073 = 19*214 + 7; hence not 19 divides 4073 by NAT_4:9;
    4073 = 23*177 + 2; hence not 23 divides 4073 by NAT_4:9;
    4073 = 29*140 + 13; hence not 29 divides 4073 by NAT_4:9;
    4073 = 31*131 + 12; hence not 31 divides 4073 by NAT_4:9;
    4073 = 37*110 + 3; hence not 37 divides 4073 by NAT_4:9;
    4073 = 41*99 + 14; hence not 41 divides 4073 by NAT_4:9;
    4073 = 43*94 + 31; hence not 43 divides 4073 by NAT_4:9;
    4073 = 47*86 + 31; hence not 47 divides 4073 by NAT_4:9;
    4073 = 53*76 + 45; hence not 53 divides 4073 by NAT_4:9;
    4073 = 59*69 + 2; hence not 59 divides 4073 by NAT_4:9;
    4073 = 61*66 + 47; hence not 61 divides 4073 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4073 & n is prime
  holds not n divides 4073 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
