
theorem
  1867 is prime
proof
  now
    1867 = 2*933 + 1; hence not 2 divides 1867 by NAT_4:9;
    1867 = 3*622 + 1; hence not 3 divides 1867 by NAT_4:9;
    1867 = 5*373 + 2; hence not 5 divides 1867 by NAT_4:9;
    1867 = 7*266 + 5; hence not 7 divides 1867 by NAT_4:9;
    1867 = 11*169 + 8; hence not 11 divides 1867 by NAT_4:9;
    1867 = 13*143 + 8; hence not 13 divides 1867 by NAT_4:9;
    1867 = 17*109 + 14; hence not 17 divides 1867 by NAT_4:9;
    1867 = 19*98 + 5; hence not 19 divides 1867 by NAT_4:9;
    1867 = 23*81 + 4; hence not 23 divides 1867 by NAT_4:9;
    1867 = 29*64 + 11; hence not 29 divides 1867 by NAT_4:9;
    1867 = 31*60 + 7; hence not 31 divides 1867 by NAT_4:9;
    1867 = 37*50 + 17; hence not 37 divides 1867 by NAT_4:9;
    1867 = 41*45 + 22; hence not 41 divides 1867 by NAT_4:9;
    1867 = 43*43 + 18; hence not 43 divides 1867 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1867 & n is prime
  holds not n divides 1867 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
