
theorem
  7829 is prime
proof
  now
    7829 = 2*3914 + 1; hence not 2 divides 7829 by NAT_4:9;
    7829 = 3*2609 + 2; hence not 3 divides 7829 by NAT_4:9;
    7829 = 5*1565 + 4; hence not 5 divides 7829 by NAT_4:9;
    7829 = 7*1118 + 3; hence not 7 divides 7829 by NAT_4:9;
    7829 = 11*711 + 8; hence not 11 divides 7829 by NAT_4:9;
    7829 = 13*602 + 3; hence not 13 divides 7829 by NAT_4:9;
    7829 = 17*460 + 9; hence not 17 divides 7829 by NAT_4:9;
    7829 = 19*412 + 1; hence not 19 divides 7829 by NAT_4:9;
    7829 = 23*340 + 9; hence not 23 divides 7829 by NAT_4:9;
    7829 = 29*269 + 28; hence not 29 divides 7829 by NAT_4:9;
    7829 = 31*252 + 17; hence not 31 divides 7829 by NAT_4:9;
    7829 = 37*211 + 22; hence not 37 divides 7829 by NAT_4:9;
    7829 = 41*190 + 39; hence not 41 divides 7829 by NAT_4:9;
    7829 = 43*182 + 3; hence not 43 divides 7829 by NAT_4:9;
    7829 = 47*166 + 27; hence not 47 divides 7829 by NAT_4:9;
    7829 = 53*147 + 38; hence not 53 divides 7829 by NAT_4:9;
    7829 = 59*132 + 41; hence not 59 divides 7829 by NAT_4:9;
    7829 = 61*128 + 21; hence not 61 divides 7829 by NAT_4:9;
    7829 = 67*116 + 57; hence not 67 divides 7829 by NAT_4:9;
    7829 = 71*110 + 19; hence not 71 divides 7829 by NAT_4:9;
    7829 = 73*107 + 18; hence not 73 divides 7829 by NAT_4:9;
    7829 = 79*99 + 8; hence not 79 divides 7829 by NAT_4:9;
    7829 = 83*94 + 27; hence not 83 divides 7829 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7829 & n is prime
  holds not n divides 7829 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
