
theorem
  8429 is prime
proof
  now
    8429 = 2*4214 + 1; hence not 2 divides 8429 by NAT_4:9;
    8429 = 3*2809 + 2; hence not 3 divides 8429 by NAT_4:9;
    8429 = 5*1685 + 4; hence not 5 divides 8429 by NAT_4:9;
    8429 = 7*1204 + 1; hence not 7 divides 8429 by NAT_4:9;
    8429 = 11*766 + 3; hence not 11 divides 8429 by NAT_4:9;
    8429 = 13*648 + 5; hence not 13 divides 8429 by NAT_4:9;
    8429 = 17*495 + 14; hence not 17 divides 8429 by NAT_4:9;
    8429 = 19*443 + 12; hence not 19 divides 8429 by NAT_4:9;
    8429 = 23*366 + 11; hence not 23 divides 8429 by NAT_4:9;
    8429 = 29*290 + 19; hence not 29 divides 8429 by NAT_4:9;
    8429 = 31*271 + 28; hence not 31 divides 8429 by NAT_4:9;
    8429 = 37*227 + 30; hence not 37 divides 8429 by NAT_4:9;
    8429 = 41*205 + 24; hence not 41 divides 8429 by NAT_4:9;
    8429 = 43*196 + 1; hence not 43 divides 8429 by NAT_4:9;
    8429 = 47*179 + 16; hence not 47 divides 8429 by NAT_4:9;
    8429 = 53*159 + 2; hence not 53 divides 8429 by NAT_4:9;
    8429 = 59*142 + 51; hence not 59 divides 8429 by NAT_4:9;
    8429 = 61*138 + 11; hence not 61 divides 8429 by NAT_4:9;
    8429 = 67*125 + 54; hence not 67 divides 8429 by NAT_4:9;
    8429 = 71*118 + 51; hence not 71 divides 8429 by NAT_4:9;
    8429 = 73*115 + 34; hence not 73 divides 8429 by NAT_4:9;
    8429 = 79*106 + 55; hence not 79 divides 8429 by NAT_4:9;
    8429 = 83*101 + 46; hence not 83 divides 8429 by NAT_4:9;
    8429 = 89*94 + 63; hence not 89 divides 8429 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8429 & n is prime
  holds not n divides 8429 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
