
theorem
  3851 is prime
proof
  now
    3851 = 2*1925 + 1; hence not 2 divides 3851 by NAT_4:9;
    3851 = 3*1283 + 2; hence not 3 divides 3851 by NAT_4:9;
    3851 = 5*770 + 1; hence not 5 divides 3851 by NAT_4:9;
    3851 = 7*550 + 1; hence not 7 divides 3851 by NAT_4:9;
    3851 = 11*350 + 1; hence not 11 divides 3851 by NAT_4:9;
    3851 = 13*296 + 3; hence not 13 divides 3851 by NAT_4:9;
    3851 = 17*226 + 9; hence not 17 divides 3851 by NAT_4:9;
    3851 = 19*202 + 13; hence not 19 divides 3851 by NAT_4:9;
    3851 = 23*167 + 10; hence not 23 divides 3851 by NAT_4:9;
    3851 = 29*132 + 23; hence not 29 divides 3851 by NAT_4:9;
    3851 = 31*124 + 7; hence not 31 divides 3851 by NAT_4:9;
    3851 = 37*104 + 3; hence not 37 divides 3851 by NAT_4:9;
    3851 = 41*93 + 38; hence not 41 divides 3851 by NAT_4:9;
    3851 = 43*89 + 24; hence not 43 divides 3851 by NAT_4:9;
    3851 = 47*81 + 44; hence not 47 divides 3851 by NAT_4:9;
    3851 = 53*72 + 35; hence not 53 divides 3851 by NAT_4:9;
    3851 = 59*65 + 16; hence not 59 divides 3851 by NAT_4:9;
    3851 = 61*63 + 8; hence not 61 divides 3851 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3851 & n is prime
  holds not n divides 3851 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
