
theorem
  3917 is prime
proof
  now
    3917 = 2*1958 + 1; hence not 2 divides 3917 by NAT_4:9;
    3917 = 3*1305 + 2; hence not 3 divides 3917 by NAT_4:9;
    3917 = 5*783 + 2; hence not 5 divides 3917 by NAT_4:9;
    3917 = 7*559 + 4; hence not 7 divides 3917 by NAT_4:9;
    3917 = 11*356 + 1; hence not 11 divides 3917 by NAT_4:9;
    3917 = 13*301 + 4; hence not 13 divides 3917 by NAT_4:9;
    3917 = 17*230 + 7; hence not 17 divides 3917 by NAT_4:9;
    3917 = 19*206 + 3; hence not 19 divides 3917 by NAT_4:9;
    3917 = 23*170 + 7; hence not 23 divides 3917 by NAT_4:9;
    3917 = 29*135 + 2; hence not 29 divides 3917 by NAT_4:9;
    3917 = 31*126 + 11; hence not 31 divides 3917 by NAT_4:9;
    3917 = 37*105 + 32; hence not 37 divides 3917 by NAT_4:9;
    3917 = 41*95 + 22; hence not 41 divides 3917 by NAT_4:9;
    3917 = 43*91 + 4; hence not 43 divides 3917 by NAT_4:9;
    3917 = 47*83 + 16; hence not 47 divides 3917 by NAT_4:9;
    3917 = 53*73 + 48; hence not 53 divides 3917 by NAT_4:9;
    3917 = 59*66 + 23; hence not 59 divides 3917 by NAT_4:9;
    3917 = 61*64 + 13; hence not 61 divides 3917 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3917 & n is prime
  holds not n divides 3917 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
