
theorem
  3803 is prime
proof
  now
    3803 = 2*1901 + 1; hence not 2 divides 3803 by NAT_4:9;
    3803 = 3*1267 + 2; hence not 3 divides 3803 by NAT_4:9;
    3803 = 5*760 + 3; hence not 5 divides 3803 by NAT_4:9;
    3803 = 7*543 + 2; hence not 7 divides 3803 by NAT_4:9;
    3803 = 11*345 + 8; hence not 11 divides 3803 by NAT_4:9;
    3803 = 13*292 + 7; hence not 13 divides 3803 by NAT_4:9;
    3803 = 17*223 + 12; hence not 17 divides 3803 by NAT_4:9;
    3803 = 19*200 + 3; hence not 19 divides 3803 by NAT_4:9;
    3803 = 23*165 + 8; hence not 23 divides 3803 by NAT_4:9;
    3803 = 29*131 + 4; hence not 29 divides 3803 by NAT_4:9;
    3803 = 31*122 + 21; hence not 31 divides 3803 by NAT_4:9;
    3803 = 37*102 + 29; hence not 37 divides 3803 by NAT_4:9;
    3803 = 41*92 + 31; hence not 41 divides 3803 by NAT_4:9;
    3803 = 43*88 + 19; hence not 43 divides 3803 by NAT_4:9;
    3803 = 47*80 + 43; hence not 47 divides 3803 by NAT_4:9;
    3803 = 53*71 + 40; hence not 53 divides 3803 by NAT_4:9;
    3803 = 59*64 + 27; hence not 59 divides 3803 by NAT_4:9;
    3803 = 61*62 + 21; hence not 61 divides 3803 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3803 & n is prime
  holds not n divides 3803 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
