
theorem
  1327 is prime
proof
  now
    1327 = 2*663 + 1; hence not 2 divides 1327 by NAT_4:9;
    1327 = 3*442 + 1; hence not 3 divides 1327 by NAT_4:9;
    1327 = 5*265 + 2; hence not 5 divides 1327 by NAT_4:9;
    1327 = 7*189 + 4; hence not 7 divides 1327 by NAT_4:9;
    1327 = 11*120 + 7; hence not 11 divides 1327 by NAT_4:9;
    1327 = 13*102 + 1; hence not 13 divides 1327 by NAT_4:9;
    1327 = 17*78 + 1; hence not 17 divides 1327 by NAT_4:9;
    1327 = 19*69 + 16; hence not 19 divides 1327 by NAT_4:9;
    1327 = 23*57 + 16; hence not 23 divides 1327 by NAT_4:9;
    1327 = 29*45 + 22; hence not 29 divides 1327 by NAT_4:9;
    1327 = 31*42 + 25; hence not 31 divides 1327 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1327 & n is prime
  holds not n divides 1327 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
