
theorem
  2357 is prime
proof
  now
    2357 = 2*1178 + 1; hence not 2 divides 2357 by NAT_4:9;
    2357 = 3*785 + 2; hence not 3 divides 2357 by NAT_4:9;
    2357 = 5*471 + 2; hence not 5 divides 2357 by NAT_4:9;
    2357 = 7*336 + 5; hence not 7 divides 2357 by NAT_4:9;
    2357 = 11*214 + 3; hence not 11 divides 2357 by NAT_4:9;
    2357 = 13*181 + 4; hence not 13 divides 2357 by NAT_4:9;
    2357 = 17*138 + 11; hence not 17 divides 2357 by NAT_4:9;
    2357 = 19*124 + 1; hence not 19 divides 2357 by NAT_4:9;
    2357 = 23*102 + 11; hence not 23 divides 2357 by NAT_4:9;
    2357 = 29*81 + 8; hence not 29 divides 2357 by NAT_4:9;
    2357 = 31*76 + 1; hence not 31 divides 2357 by NAT_4:9;
    2357 = 37*63 + 26; hence not 37 divides 2357 by NAT_4:9;
    2357 = 41*57 + 20; hence not 41 divides 2357 by NAT_4:9;
    2357 = 43*54 + 35; hence not 43 divides 2357 by NAT_4:9;
    2357 = 47*50 + 7; hence not 47 divides 2357 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2357 & n is prime
  holds not n divides 2357 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
