
theorem
  2707 is prime
proof
  now
    2707 = 2*1353 + 1; hence not 2 divides 2707 by NAT_4:9;
    2707 = 3*902 + 1; hence not 3 divides 2707 by NAT_4:9;
    2707 = 5*541 + 2; hence not 5 divides 2707 by NAT_4:9;
    2707 = 7*386 + 5; hence not 7 divides 2707 by NAT_4:9;
    2707 = 11*246 + 1; hence not 11 divides 2707 by NAT_4:9;
    2707 = 13*208 + 3; hence not 13 divides 2707 by NAT_4:9;
    2707 = 17*159 + 4; hence not 17 divides 2707 by NAT_4:9;
    2707 = 19*142 + 9; hence not 19 divides 2707 by NAT_4:9;
    2707 = 23*117 + 16; hence not 23 divides 2707 by NAT_4:9;
    2707 = 29*93 + 10; hence not 29 divides 2707 by NAT_4:9;
    2707 = 31*87 + 10; hence not 31 divides 2707 by NAT_4:9;
    2707 = 37*73 + 6; hence not 37 divides 2707 by NAT_4:9;
    2707 = 41*66 + 1; hence not 41 divides 2707 by NAT_4:9;
    2707 = 43*62 + 41; hence not 43 divides 2707 by NAT_4:9;
    2707 = 47*57 + 28; hence not 47 divides 2707 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2707 & n is prime
  holds not n divides 2707 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
