
theorem
  9431 is prime
proof
  now
    9431 = 2*4715 + 1; hence not 2 divides 9431 by NAT_4:9;
    9431 = 3*3143 + 2; hence not 3 divides 9431 by NAT_4:9;
    9431 = 5*1886 + 1; hence not 5 divides 9431 by NAT_4:9;
    9431 = 7*1347 + 2; hence not 7 divides 9431 by NAT_4:9;
    9431 = 11*857 + 4; hence not 11 divides 9431 by NAT_4:9;
    9431 = 13*725 + 6; hence not 13 divides 9431 by NAT_4:9;
    9431 = 17*554 + 13; hence not 17 divides 9431 by NAT_4:9;
    9431 = 19*496 + 7; hence not 19 divides 9431 by NAT_4:9;
    9431 = 23*410 + 1; hence not 23 divides 9431 by NAT_4:9;
    9431 = 29*325 + 6; hence not 29 divides 9431 by NAT_4:9;
    9431 = 31*304 + 7; hence not 31 divides 9431 by NAT_4:9;
    9431 = 37*254 + 33; hence not 37 divides 9431 by NAT_4:9;
    9431 = 41*230 + 1; hence not 41 divides 9431 by NAT_4:9;
    9431 = 43*219 + 14; hence not 43 divides 9431 by NAT_4:9;
    9431 = 47*200 + 31; hence not 47 divides 9431 by NAT_4:9;
    9431 = 53*177 + 50; hence not 53 divides 9431 by NAT_4:9;
    9431 = 59*159 + 50; hence not 59 divides 9431 by NAT_4:9;
    9431 = 61*154 + 37; hence not 61 divides 9431 by NAT_4:9;
    9431 = 67*140 + 51; hence not 67 divides 9431 by NAT_4:9;
    9431 = 71*132 + 59; hence not 71 divides 9431 by NAT_4:9;
    9431 = 73*129 + 14; hence not 73 divides 9431 by NAT_4:9;
    9431 = 79*119 + 30; hence not 79 divides 9431 by NAT_4:9;
    9431 = 83*113 + 52; hence not 83 divides 9431 by NAT_4:9;
    9431 = 89*105 + 86; hence not 89 divides 9431 by NAT_4:9;
    9431 = 97*97 + 22; hence not 97 divides 9431 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9431 & n is prime
  holds not n divides 9431 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
