
theorem
  2741 is prime
proof
  now
    2741 = 2*1370 + 1; hence not 2 divides 2741 by NAT_4:9;
    2741 = 3*913 + 2; hence not 3 divides 2741 by NAT_4:9;
    2741 = 5*548 + 1; hence not 5 divides 2741 by NAT_4:9;
    2741 = 7*391 + 4; hence not 7 divides 2741 by NAT_4:9;
    2741 = 11*249 + 2; hence not 11 divides 2741 by NAT_4:9;
    2741 = 13*210 + 11; hence not 13 divides 2741 by NAT_4:9;
    2741 = 17*161 + 4; hence not 17 divides 2741 by NAT_4:9;
    2741 = 19*144 + 5; hence not 19 divides 2741 by NAT_4:9;
    2741 = 23*119 + 4; hence not 23 divides 2741 by NAT_4:9;
    2741 = 29*94 + 15; hence not 29 divides 2741 by NAT_4:9;
    2741 = 31*88 + 13; hence not 31 divides 2741 by NAT_4:9;
    2741 = 37*74 + 3; hence not 37 divides 2741 by NAT_4:9;
    2741 = 41*66 + 35; hence not 41 divides 2741 by NAT_4:9;
    2741 = 43*63 + 32; hence not 43 divides 2741 by NAT_4:9;
    2741 = 47*58 + 15; hence not 47 divides 2741 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2741 & n is prime
  holds not n divides 2741 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
