
theorem
  1931 is prime
proof
  now
    1931 = 2*965 + 1; hence not 2 divides 1931 by NAT_4:9;
    1931 = 3*643 + 2; hence not 3 divides 1931 by NAT_4:9;
    1931 = 5*386 + 1; hence not 5 divides 1931 by NAT_4:9;
    1931 = 7*275 + 6; hence not 7 divides 1931 by NAT_4:9;
    1931 = 11*175 + 6; hence not 11 divides 1931 by NAT_4:9;
    1931 = 13*148 + 7; hence not 13 divides 1931 by NAT_4:9;
    1931 = 17*113 + 10; hence not 17 divides 1931 by NAT_4:9;
    1931 = 19*101 + 12; hence not 19 divides 1931 by NAT_4:9;
    1931 = 23*83 + 22; hence not 23 divides 1931 by NAT_4:9;
    1931 = 29*66 + 17; hence not 29 divides 1931 by NAT_4:9;
    1931 = 31*62 + 9; hence not 31 divides 1931 by NAT_4:9;
    1931 = 37*52 + 7; hence not 37 divides 1931 by NAT_4:9;
    1931 = 41*47 + 4; hence not 41 divides 1931 by NAT_4:9;
    1931 = 43*44 + 39; hence not 43 divides 1931 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1931 & n is prime
  holds not n divides 1931 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
