
theorem
  1933 is prime
proof
  now
    1933 = 2*966 + 1; hence not 2 divides 1933 by NAT_4:9;
    1933 = 3*644 + 1; hence not 3 divides 1933 by NAT_4:9;
    1933 = 5*386 + 3; hence not 5 divides 1933 by NAT_4:9;
    1933 = 7*276 + 1; hence not 7 divides 1933 by NAT_4:9;
    1933 = 11*175 + 8; hence not 11 divides 1933 by NAT_4:9;
    1933 = 13*148 + 9; hence not 13 divides 1933 by NAT_4:9;
    1933 = 17*113 + 12; hence not 17 divides 1933 by NAT_4:9;
    1933 = 19*101 + 14; hence not 19 divides 1933 by NAT_4:9;
    1933 = 23*84 + 1; hence not 23 divides 1933 by NAT_4:9;
    1933 = 29*66 + 19; hence not 29 divides 1933 by NAT_4:9;
    1933 = 31*62 + 11; hence not 31 divides 1933 by NAT_4:9;
    1933 = 37*52 + 9; hence not 37 divides 1933 by NAT_4:9;
    1933 = 41*47 + 6; hence not 41 divides 1933 by NAT_4:9;
    1933 = 43*44 + 41; hence not 43 divides 1933 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1933 & n is prime
  holds not n divides 1933 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
