
theorem
  3457 is prime
proof
  now
    3457 = 2*1728 + 1; hence not 2 divides 3457 by NAT_4:9;
    3457 = 3*1152 + 1; hence not 3 divides 3457 by NAT_4:9;
    3457 = 5*691 + 2; hence not 5 divides 3457 by NAT_4:9;
    3457 = 7*493 + 6; hence not 7 divides 3457 by NAT_4:9;
    3457 = 11*314 + 3; hence not 11 divides 3457 by NAT_4:9;
    3457 = 13*265 + 12; hence not 13 divides 3457 by NAT_4:9;
    3457 = 17*203 + 6; hence not 17 divides 3457 by NAT_4:9;
    3457 = 19*181 + 18; hence not 19 divides 3457 by NAT_4:9;
    3457 = 23*150 + 7; hence not 23 divides 3457 by NAT_4:9;
    3457 = 29*119 + 6; hence not 29 divides 3457 by NAT_4:9;
    3457 = 31*111 + 16; hence not 31 divides 3457 by NAT_4:9;
    3457 = 37*93 + 16; hence not 37 divides 3457 by NAT_4:9;
    3457 = 41*84 + 13; hence not 41 divides 3457 by NAT_4:9;
    3457 = 43*80 + 17; hence not 43 divides 3457 by NAT_4:9;
    3457 = 47*73 + 26; hence not 47 divides 3457 by NAT_4:9;
    3457 = 53*65 + 12; hence not 53 divides 3457 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3457 & n is prime
  holds not n divides 3457 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
