
theorem
  3907 is prime
proof
  now
    3907 = 2*1953 + 1; hence not 2 divides 3907 by NAT_4:9;
    3907 = 3*1302 + 1; hence not 3 divides 3907 by NAT_4:9;
    3907 = 5*781 + 2; hence not 5 divides 3907 by NAT_4:9;
    3907 = 7*558 + 1; hence not 7 divides 3907 by NAT_4:9;
    3907 = 11*355 + 2; hence not 11 divides 3907 by NAT_4:9;
    3907 = 13*300 + 7; hence not 13 divides 3907 by NAT_4:9;
    3907 = 17*229 + 14; hence not 17 divides 3907 by NAT_4:9;
    3907 = 19*205 + 12; hence not 19 divides 3907 by NAT_4:9;
    3907 = 23*169 + 20; hence not 23 divides 3907 by NAT_4:9;
    3907 = 29*134 + 21; hence not 29 divides 3907 by NAT_4:9;
    3907 = 31*126 + 1; hence not 31 divides 3907 by NAT_4:9;
    3907 = 37*105 + 22; hence not 37 divides 3907 by NAT_4:9;
    3907 = 41*95 + 12; hence not 41 divides 3907 by NAT_4:9;
    3907 = 43*90 + 37; hence not 43 divides 3907 by NAT_4:9;
    3907 = 47*83 + 6; hence not 47 divides 3907 by NAT_4:9;
    3907 = 53*73 + 38; hence not 53 divides 3907 by NAT_4:9;
    3907 = 59*66 + 13; hence not 59 divides 3907 by NAT_4:9;
    3907 = 61*64 + 3; hence not 61 divides 3907 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3907 & n is prime
  holds not n divides 3907 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
