
theorem
  3923 is prime
proof
  now
    3923 = 2*1961 + 1; hence not 2 divides 3923 by NAT_4:9;
    3923 = 3*1307 + 2; hence not 3 divides 3923 by NAT_4:9;
    3923 = 5*784 + 3; hence not 5 divides 3923 by NAT_4:9;
    3923 = 7*560 + 3; hence not 7 divides 3923 by NAT_4:9;
    3923 = 11*356 + 7; hence not 11 divides 3923 by NAT_4:9;
    3923 = 13*301 + 10; hence not 13 divides 3923 by NAT_4:9;
    3923 = 17*230 + 13; hence not 17 divides 3923 by NAT_4:9;
    3923 = 19*206 + 9; hence not 19 divides 3923 by NAT_4:9;
    3923 = 23*170 + 13; hence not 23 divides 3923 by NAT_4:9;
    3923 = 29*135 + 8; hence not 29 divides 3923 by NAT_4:9;
    3923 = 31*126 + 17; hence not 31 divides 3923 by NAT_4:9;
    3923 = 37*106 + 1; hence not 37 divides 3923 by NAT_4:9;
    3923 = 41*95 + 28; hence not 41 divides 3923 by NAT_4:9;
    3923 = 43*91 + 10; hence not 43 divides 3923 by NAT_4:9;
    3923 = 47*83 + 22; hence not 47 divides 3923 by NAT_4:9;
    3923 = 53*74 + 1; hence not 53 divides 3923 by NAT_4:9;
    3923 = 59*66 + 29; hence not 59 divides 3923 by NAT_4:9;
    3923 = 61*64 + 19; hence not 61 divides 3923 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3923 & n is prime
  holds not n divides 3923 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
