
theorem
  7841 is prime
proof
  now
    7841 = 2*3920 + 1; hence not 2 divides 7841 by NAT_4:9;
    7841 = 3*2613 + 2; hence not 3 divides 7841 by NAT_4:9;
    7841 = 5*1568 + 1; hence not 5 divides 7841 by NAT_4:9;
    7841 = 7*1120 + 1; hence not 7 divides 7841 by NAT_4:9;
    7841 = 11*712 + 9; hence not 11 divides 7841 by NAT_4:9;
    7841 = 13*603 + 2; hence not 13 divides 7841 by NAT_4:9;
    7841 = 17*461 + 4; hence not 17 divides 7841 by NAT_4:9;
    7841 = 19*412 + 13; hence not 19 divides 7841 by NAT_4:9;
    7841 = 23*340 + 21; hence not 23 divides 7841 by NAT_4:9;
    7841 = 29*270 + 11; hence not 29 divides 7841 by NAT_4:9;
    7841 = 31*252 + 29; hence not 31 divides 7841 by NAT_4:9;
    7841 = 37*211 + 34; hence not 37 divides 7841 by NAT_4:9;
    7841 = 41*191 + 10; hence not 41 divides 7841 by NAT_4:9;
    7841 = 43*182 + 15; hence not 43 divides 7841 by NAT_4:9;
    7841 = 47*166 + 39; hence not 47 divides 7841 by NAT_4:9;
    7841 = 53*147 + 50; hence not 53 divides 7841 by NAT_4:9;
    7841 = 59*132 + 53; hence not 59 divides 7841 by NAT_4:9;
    7841 = 61*128 + 33; hence not 61 divides 7841 by NAT_4:9;
    7841 = 67*117 + 2; hence not 67 divides 7841 by NAT_4:9;
    7841 = 71*110 + 31; hence not 71 divides 7841 by NAT_4:9;
    7841 = 73*107 + 30; hence not 73 divides 7841 by NAT_4:9;
    7841 = 79*99 + 20; hence not 79 divides 7841 by NAT_4:9;
    7841 = 83*94 + 39; hence not 83 divides 7841 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7841 & n is prime
  holds not n divides 7841 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
