
theorem
  1847 is prime
proof
  now
    1847 = 2*923 + 1; hence not 2 divides 1847 by NAT_4:9;
    1847 = 3*615 + 2; hence not 3 divides 1847 by NAT_4:9;
    1847 = 5*369 + 2; hence not 5 divides 1847 by NAT_4:9;
    1847 = 7*263 + 6; hence not 7 divides 1847 by NAT_4:9;
    1847 = 11*167 + 10; hence not 11 divides 1847 by NAT_4:9;
    1847 = 13*142 + 1; hence not 13 divides 1847 by NAT_4:9;
    1847 = 17*108 + 11; hence not 17 divides 1847 by NAT_4:9;
    1847 = 19*97 + 4; hence not 19 divides 1847 by NAT_4:9;
    1847 = 23*80 + 7; hence not 23 divides 1847 by NAT_4:9;
    1847 = 29*63 + 20; hence not 29 divides 1847 by NAT_4:9;
    1847 = 31*59 + 18; hence not 31 divides 1847 by NAT_4:9;
    1847 = 37*49 + 34; hence not 37 divides 1847 by NAT_4:9;
    1847 = 41*45 + 2; hence not 41 divides 1847 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1847 & n is prime
  holds not n divides 1847 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
