
theorem
  7877 is prime
proof
  now
    7877 = 2*3938 + 1; hence not 2 divides 7877 by NAT_4:9;
    7877 = 3*2625 + 2; hence not 3 divides 7877 by NAT_4:9;
    7877 = 5*1575 + 2; hence not 5 divides 7877 by NAT_4:9;
    7877 = 7*1125 + 2; hence not 7 divides 7877 by NAT_4:9;
    7877 = 11*716 + 1; hence not 11 divides 7877 by NAT_4:9;
    7877 = 13*605 + 12; hence not 13 divides 7877 by NAT_4:9;
    7877 = 17*463 + 6; hence not 17 divides 7877 by NAT_4:9;
    7877 = 19*414 + 11; hence not 19 divides 7877 by NAT_4:9;
    7877 = 23*342 + 11; hence not 23 divides 7877 by NAT_4:9;
    7877 = 29*271 + 18; hence not 29 divides 7877 by NAT_4:9;
    7877 = 31*254 + 3; hence not 31 divides 7877 by NAT_4:9;
    7877 = 37*212 + 33; hence not 37 divides 7877 by NAT_4:9;
    7877 = 41*192 + 5; hence not 41 divides 7877 by NAT_4:9;
    7877 = 43*183 + 8; hence not 43 divides 7877 by NAT_4:9;
    7877 = 47*167 + 28; hence not 47 divides 7877 by NAT_4:9;
    7877 = 53*148 + 33; hence not 53 divides 7877 by NAT_4:9;
    7877 = 59*133 + 30; hence not 59 divides 7877 by NAT_4:9;
    7877 = 61*129 + 8; hence not 61 divides 7877 by NAT_4:9;
    7877 = 67*117 + 38; hence not 67 divides 7877 by NAT_4:9;
    7877 = 71*110 + 67; hence not 71 divides 7877 by NAT_4:9;
    7877 = 73*107 + 66; hence not 73 divides 7877 by NAT_4:9;
    7877 = 79*99 + 56; hence not 79 divides 7877 by NAT_4:9;
    7877 = 83*94 + 75; hence not 83 divides 7877 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7877 & n is prime
  holds not n divides 7877 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
