
theorem
  7853 is prime
proof
  now
    7853 = 2*3926 + 1; hence not 2 divides 7853 by NAT_4:9;
    7853 = 3*2617 + 2; hence not 3 divides 7853 by NAT_4:9;
    7853 = 5*1570 + 3; hence not 5 divides 7853 by NAT_4:9;
    7853 = 7*1121 + 6; hence not 7 divides 7853 by NAT_4:9;
    7853 = 11*713 + 10; hence not 11 divides 7853 by NAT_4:9;
    7853 = 13*604 + 1; hence not 13 divides 7853 by NAT_4:9;
    7853 = 17*461 + 16; hence not 17 divides 7853 by NAT_4:9;
    7853 = 19*413 + 6; hence not 19 divides 7853 by NAT_4:9;
    7853 = 23*341 + 10; hence not 23 divides 7853 by NAT_4:9;
    7853 = 29*270 + 23; hence not 29 divides 7853 by NAT_4:9;
    7853 = 31*253 + 10; hence not 31 divides 7853 by NAT_4:9;
    7853 = 37*212 + 9; hence not 37 divides 7853 by NAT_4:9;
    7853 = 41*191 + 22; hence not 41 divides 7853 by NAT_4:9;
    7853 = 43*182 + 27; hence not 43 divides 7853 by NAT_4:9;
    7853 = 47*167 + 4; hence not 47 divides 7853 by NAT_4:9;
    7853 = 53*148 + 9; hence not 53 divides 7853 by NAT_4:9;
    7853 = 59*133 + 6; hence not 59 divides 7853 by NAT_4:9;
    7853 = 61*128 + 45; hence not 61 divides 7853 by NAT_4:9;
    7853 = 67*117 + 14; hence not 67 divides 7853 by NAT_4:9;
    7853 = 71*110 + 43; hence not 71 divides 7853 by NAT_4:9;
    7853 = 73*107 + 42; hence not 73 divides 7853 by NAT_4:9;
    7853 = 79*99 + 32; hence not 79 divides 7853 by NAT_4:9;
    7853 = 83*94 + 51; hence not 83 divides 7853 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7853 & n is prime
  holds not n divides 7853 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
