
theorem
  8431 is prime
proof
  now
    8431 = 2*4215 + 1; hence not 2 divides 8431 by NAT_4:9;
    8431 = 3*2810 + 1; hence not 3 divides 8431 by NAT_4:9;
    8431 = 5*1686 + 1; hence not 5 divides 8431 by NAT_4:9;
    8431 = 7*1204 + 3; hence not 7 divides 8431 by NAT_4:9;
    8431 = 11*766 + 5; hence not 11 divides 8431 by NAT_4:9;
    8431 = 13*648 + 7; hence not 13 divides 8431 by NAT_4:9;
    8431 = 17*495 + 16; hence not 17 divides 8431 by NAT_4:9;
    8431 = 19*443 + 14; hence not 19 divides 8431 by NAT_4:9;
    8431 = 23*366 + 13; hence not 23 divides 8431 by NAT_4:9;
    8431 = 29*290 + 21; hence not 29 divides 8431 by NAT_4:9;
    8431 = 31*271 + 30; hence not 31 divides 8431 by NAT_4:9;
    8431 = 37*227 + 32; hence not 37 divides 8431 by NAT_4:9;
    8431 = 41*205 + 26; hence not 41 divides 8431 by NAT_4:9;
    8431 = 43*196 + 3; hence not 43 divides 8431 by NAT_4:9;
    8431 = 47*179 + 18; hence not 47 divides 8431 by NAT_4:9;
    8431 = 53*159 + 4; hence not 53 divides 8431 by NAT_4:9;
    8431 = 59*142 + 53; hence not 59 divides 8431 by NAT_4:9;
    8431 = 61*138 + 13; hence not 61 divides 8431 by NAT_4:9;
    8431 = 67*125 + 56; hence not 67 divides 8431 by NAT_4:9;
    8431 = 71*118 + 53; hence not 71 divides 8431 by NAT_4:9;
    8431 = 73*115 + 36; hence not 73 divides 8431 by NAT_4:9;
    8431 = 79*106 + 57; hence not 79 divides 8431 by NAT_4:9;
    8431 = 83*101 + 48; hence not 83 divides 8431 by NAT_4:9;
    8431 = 89*94 + 65; hence not 89 divides 8431 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8431 & n is prime
  holds not n divides 8431 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
