
theorem
  2801 is prime
proof
  now
    2801 = 2*1400 + 1; hence not 2 divides 2801 by NAT_4:9;
    2801 = 3*933 + 2; hence not 3 divides 2801 by NAT_4:9;
    2801 = 5*560 + 1; hence not 5 divides 2801 by NAT_4:9;
    2801 = 7*400 + 1; hence not 7 divides 2801 by NAT_4:9;
    2801 = 11*254 + 7; hence not 11 divides 2801 by NAT_4:9;
    2801 = 13*215 + 6; hence not 13 divides 2801 by NAT_4:9;
    2801 = 17*164 + 13; hence not 17 divides 2801 by NAT_4:9;
    2801 = 19*147 + 8; hence not 19 divides 2801 by NAT_4:9;
    2801 = 23*121 + 18; hence not 23 divides 2801 by NAT_4:9;
    2801 = 29*96 + 17; hence not 29 divides 2801 by NAT_4:9;
    2801 = 31*90 + 11; hence not 31 divides 2801 by NAT_4:9;
    2801 = 37*75 + 26; hence not 37 divides 2801 by NAT_4:9;
    2801 = 41*68 + 13; hence not 41 divides 2801 by NAT_4:9;
    2801 = 43*65 + 6; hence not 43 divides 2801 by NAT_4:9;
    2801 = 47*59 + 28; hence not 47 divides 2801 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2801 & n is prime
  holds not n divides 2801 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
