
theorem
  4003 is prime
proof
  now
    4003 = 2*2001 + 1; hence not 2 divides 4003 by NAT_4:9;
    4003 = 3*1334 + 1; hence not 3 divides 4003 by NAT_4:9;
    4003 = 5*800 + 3; hence not 5 divides 4003 by NAT_4:9;
    4003 = 7*571 + 6; hence not 7 divides 4003 by NAT_4:9;
    4003 = 11*363 + 10; hence not 11 divides 4003 by NAT_4:9;
    4003 = 13*307 + 12; hence not 13 divides 4003 by NAT_4:9;
    4003 = 17*235 + 8; hence not 17 divides 4003 by NAT_4:9;
    4003 = 19*210 + 13; hence not 19 divides 4003 by NAT_4:9;
    4003 = 23*174 + 1; hence not 23 divides 4003 by NAT_4:9;
    4003 = 29*138 + 1; hence not 29 divides 4003 by NAT_4:9;
    4003 = 31*129 + 4; hence not 31 divides 4003 by NAT_4:9;
    4003 = 37*108 + 7; hence not 37 divides 4003 by NAT_4:9;
    4003 = 41*97 + 26; hence not 41 divides 4003 by NAT_4:9;
    4003 = 43*93 + 4; hence not 43 divides 4003 by NAT_4:9;
    4003 = 47*85 + 8; hence not 47 divides 4003 by NAT_4:9;
    4003 = 53*75 + 28; hence not 53 divides 4003 by NAT_4:9;
    4003 = 59*67 + 50; hence not 59 divides 4003 by NAT_4:9;
    4003 = 61*65 + 38; hence not 61 divides 4003 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4003 & n is prime
  holds not n divides 4003 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
