
theorem
  1879 is prime
proof
  now
    1879 = 2*939 + 1; hence not 2 divides 1879 by NAT_4:9;
    1879 = 3*626 + 1; hence not 3 divides 1879 by NAT_4:9;
    1879 = 5*375 + 4; hence not 5 divides 1879 by NAT_4:9;
    1879 = 7*268 + 3; hence not 7 divides 1879 by NAT_4:9;
    1879 = 11*170 + 9; hence not 11 divides 1879 by NAT_4:9;
    1879 = 13*144 + 7; hence not 13 divides 1879 by NAT_4:9;
    1879 = 17*110 + 9; hence not 17 divides 1879 by NAT_4:9;
    1879 = 19*98 + 17; hence not 19 divides 1879 by NAT_4:9;
    1879 = 23*81 + 16; hence not 23 divides 1879 by NAT_4:9;
    1879 = 29*64 + 23; hence not 29 divides 1879 by NAT_4:9;
    1879 = 31*60 + 19; hence not 31 divides 1879 by NAT_4:9;
    1879 = 37*50 + 29; hence not 37 divides 1879 by NAT_4:9;
    1879 = 41*45 + 34; hence not 41 divides 1879 by NAT_4:9;
    1879 = 43*43 + 30; hence not 43 divides 1879 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1879 & n is prime
  holds not n divides 1879 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
