
theorem
  3931 is prime
proof
  now
    3931 = 2*1965 + 1; hence not 2 divides 3931 by NAT_4:9;
    3931 = 3*1310 + 1; hence not 3 divides 3931 by NAT_4:9;
    3931 = 5*786 + 1; hence not 5 divides 3931 by NAT_4:9;
    3931 = 7*561 + 4; hence not 7 divides 3931 by NAT_4:9;
    3931 = 11*357 + 4; hence not 11 divides 3931 by NAT_4:9;
    3931 = 13*302 + 5; hence not 13 divides 3931 by NAT_4:9;
    3931 = 17*231 + 4; hence not 17 divides 3931 by NAT_4:9;
    3931 = 19*206 + 17; hence not 19 divides 3931 by NAT_4:9;
    3931 = 23*170 + 21; hence not 23 divides 3931 by NAT_4:9;
    3931 = 29*135 + 16; hence not 29 divides 3931 by NAT_4:9;
    3931 = 31*126 + 25; hence not 31 divides 3931 by NAT_4:9;
    3931 = 37*106 + 9; hence not 37 divides 3931 by NAT_4:9;
    3931 = 41*95 + 36; hence not 41 divides 3931 by NAT_4:9;
    3931 = 43*91 + 18; hence not 43 divides 3931 by NAT_4:9;
    3931 = 47*83 + 30; hence not 47 divides 3931 by NAT_4:9;
    3931 = 53*74 + 9; hence not 53 divides 3931 by NAT_4:9;
    3931 = 59*66 + 37; hence not 59 divides 3931 by NAT_4:9;
    3931 = 61*64 + 27; hence not 61 divides 3931 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3931 & n is prime
  holds not n divides 3931 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
