
theorem
  3877 is prime
proof
  now
    3877 = 2*1938 + 1; hence not 2 divides 3877 by NAT_4:9;
    3877 = 3*1292 + 1; hence not 3 divides 3877 by NAT_4:9;
    3877 = 5*775 + 2; hence not 5 divides 3877 by NAT_4:9;
    3877 = 7*553 + 6; hence not 7 divides 3877 by NAT_4:9;
    3877 = 11*352 + 5; hence not 11 divides 3877 by NAT_4:9;
    3877 = 13*298 + 3; hence not 13 divides 3877 by NAT_4:9;
    3877 = 17*228 + 1; hence not 17 divides 3877 by NAT_4:9;
    3877 = 19*204 + 1; hence not 19 divides 3877 by NAT_4:9;
    3877 = 23*168 + 13; hence not 23 divides 3877 by NAT_4:9;
    3877 = 29*133 + 20; hence not 29 divides 3877 by NAT_4:9;
    3877 = 31*125 + 2; hence not 31 divides 3877 by NAT_4:9;
    3877 = 37*104 + 29; hence not 37 divides 3877 by NAT_4:9;
    3877 = 41*94 + 23; hence not 41 divides 3877 by NAT_4:9;
    3877 = 43*90 + 7; hence not 43 divides 3877 by NAT_4:9;
    3877 = 47*82 + 23; hence not 47 divides 3877 by NAT_4:9;
    3877 = 53*73 + 8; hence not 53 divides 3877 by NAT_4:9;
    3877 = 59*65 + 42; hence not 59 divides 3877 by NAT_4:9;
    3877 = 61*63 + 34; hence not 61 divides 3877 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3877 & n is prime
  holds not n divides 3877 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
