
theorem
  2027 is prime
proof
  now
    2027 = 2*1013 + 1; hence not 2 divides 2027 by NAT_4:9;
    2027 = 3*675 + 2; hence not 3 divides 2027 by NAT_4:9;
    2027 = 5*405 + 2; hence not 5 divides 2027 by NAT_4:9;
    2027 = 7*289 + 4; hence not 7 divides 2027 by NAT_4:9;
    2027 = 11*184 + 3; hence not 11 divides 2027 by NAT_4:9;
    2027 = 13*155 + 12; hence not 13 divides 2027 by NAT_4:9;
    2027 = 17*119 + 4; hence not 17 divides 2027 by NAT_4:9;
    2027 = 19*106 + 13; hence not 19 divides 2027 by NAT_4:9;
    2027 = 23*88 + 3; hence not 23 divides 2027 by NAT_4:9;
    2027 = 29*69 + 26; hence not 29 divides 2027 by NAT_4:9;
    2027 = 31*65 + 12; hence not 31 divides 2027 by NAT_4:9;
    2027 = 37*54 + 29; hence not 37 divides 2027 by NAT_4:9;
    2027 = 41*49 + 18; hence not 41 divides 2027 by NAT_4:9;
    2027 = 43*47 + 6; hence not 43 divides 2027 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2027 & n is prime
  holds not n divides 2027 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
