
theorem
  2371 is prime
proof
  now
    2371 = 2*1185 + 1; hence not 2 divides 2371 by NAT_4:9;
    2371 = 3*790 + 1; hence not 3 divides 2371 by NAT_4:9;
    2371 = 5*474 + 1; hence not 5 divides 2371 by NAT_4:9;
    2371 = 7*338 + 5; hence not 7 divides 2371 by NAT_4:9;
    2371 = 11*215 + 6; hence not 11 divides 2371 by NAT_4:9;
    2371 = 13*182 + 5; hence not 13 divides 2371 by NAT_4:9;
    2371 = 17*139 + 8; hence not 17 divides 2371 by NAT_4:9;
    2371 = 19*124 + 15; hence not 19 divides 2371 by NAT_4:9;
    2371 = 23*103 + 2; hence not 23 divides 2371 by NAT_4:9;
    2371 = 29*81 + 22; hence not 29 divides 2371 by NAT_4:9;
    2371 = 31*76 + 15; hence not 31 divides 2371 by NAT_4:9;
    2371 = 37*64 + 3; hence not 37 divides 2371 by NAT_4:9;
    2371 = 41*57 + 34; hence not 41 divides 2371 by NAT_4:9;
    2371 = 43*55 + 6; hence not 43 divides 2371 by NAT_4:9;
    2371 = 47*50 + 21; hence not 47 divides 2371 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2371 & n is prime
  holds not n divides 2371 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
