
theorem
  4027 is prime
proof
  now
    4027 = 2*2013 + 1; hence not 2 divides 4027 by NAT_4:9;
    4027 = 3*1342 + 1; hence not 3 divides 4027 by NAT_4:9;
    4027 = 5*805 + 2; hence not 5 divides 4027 by NAT_4:9;
    4027 = 7*575 + 2; hence not 7 divides 4027 by NAT_4:9;
    4027 = 11*366 + 1; hence not 11 divides 4027 by NAT_4:9;
    4027 = 13*309 + 10; hence not 13 divides 4027 by NAT_4:9;
    4027 = 17*236 + 15; hence not 17 divides 4027 by NAT_4:9;
    4027 = 19*211 + 18; hence not 19 divides 4027 by NAT_4:9;
    4027 = 23*175 + 2; hence not 23 divides 4027 by NAT_4:9;
    4027 = 29*138 + 25; hence not 29 divides 4027 by NAT_4:9;
    4027 = 31*129 + 28; hence not 31 divides 4027 by NAT_4:9;
    4027 = 37*108 + 31; hence not 37 divides 4027 by NAT_4:9;
    4027 = 41*98 + 9; hence not 41 divides 4027 by NAT_4:9;
    4027 = 43*93 + 28; hence not 43 divides 4027 by NAT_4:9;
    4027 = 47*85 + 32; hence not 47 divides 4027 by NAT_4:9;
    4027 = 53*75 + 52; hence not 53 divides 4027 by NAT_4:9;
    4027 = 59*68 + 15; hence not 59 divides 4027 by NAT_4:9;
    4027 = 61*66 + 1; hence not 61 divides 4027 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4027 & n is prime
  holds not n divides 4027 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
