
theorem
  1801 is prime
proof
  now
    1801 = 2*900 + 1; hence not 2 divides 1801 by NAT_4:9;
    1801 = 3*600 + 1; hence not 3 divides 1801 by NAT_4:9;
    1801 = 5*360 + 1; hence not 5 divides 1801 by NAT_4:9;
    1801 = 7*257 + 2; hence not 7 divides 1801 by NAT_4:9;
    1801 = 11*163 + 8; hence not 11 divides 1801 by NAT_4:9;
    1801 = 13*138 + 7; hence not 13 divides 1801 by NAT_4:9;
    1801 = 17*105 + 16; hence not 17 divides 1801 by NAT_4:9;
    1801 = 19*94 + 15; hence not 19 divides 1801 by NAT_4:9;
    1801 = 23*78 + 7; hence not 23 divides 1801 by NAT_4:9;
    1801 = 29*62 + 3; hence not 29 divides 1801 by NAT_4:9;
    1801 = 31*58 + 3; hence not 31 divides 1801 by NAT_4:9;
    1801 = 37*48 + 25; hence not 37 divides 1801 by NAT_4:9;
    1801 = 41*43 + 38; hence not 41 divides 1801 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1801 & n is prime
  holds not n divides 1801 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
