
theorem
  3331 is prime
proof
  now
    3331 = 2*1665 + 1; hence not 2 divides 3331 by NAT_4:9;
    3331 = 3*1110 + 1; hence not 3 divides 3331 by NAT_4:9;
    3331 = 5*666 + 1; hence not 5 divides 3331 by NAT_4:9;
    3331 = 7*475 + 6; hence not 7 divides 3331 by NAT_4:9;
    3331 = 11*302 + 9; hence not 11 divides 3331 by NAT_4:9;
    3331 = 13*256 + 3; hence not 13 divides 3331 by NAT_4:9;
    3331 = 17*195 + 16; hence not 17 divides 3331 by NAT_4:9;
    3331 = 19*175 + 6; hence not 19 divides 3331 by NAT_4:9;
    3331 = 23*144 + 19; hence not 23 divides 3331 by NAT_4:9;
    3331 = 29*114 + 25; hence not 29 divides 3331 by NAT_4:9;
    3331 = 31*107 + 14; hence not 31 divides 3331 by NAT_4:9;
    3331 = 37*90 + 1; hence not 37 divides 3331 by NAT_4:9;
    3331 = 41*81 + 10; hence not 41 divides 3331 by NAT_4:9;
    3331 = 43*77 + 20; hence not 43 divides 3331 by NAT_4:9;
    3331 = 47*70 + 41; hence not 47 divides 3331 by NAT_4:9;
    3331 = 53*62 + 45; hence not 53 divides 3331 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3331 & n is prime
  holds not n divides 3331 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
