
theorem
  7433 is prime
proof
  now
    7433 = 2*3716 + 1; hence not 2 divides 7433 by NAT_4:9;
    7433 = 3*2477 + 2; hence not 3 divides 7433 by NAT_4:9;
    7433 = 5*1486 + 3; hence not 5 divides 7433 by NAT_4:9;
    7433 = 7*1061 + 6; hence not 7 divides 7433 by NAT_4:9;
    7433 = 11*675 + 8; hence not 11 divides 7433 by NAT_4:9;
    7433 = 13*571 + 10; hence not 13 divides 7433 by NAT_4:9;
    7433 = 17*437 + 4; hence not 17 divides 7433 by NAT_4:9;
    7433 = 19*391 + 4; hence not 19 divides 7433 by NAT_4:9;
    7433 = 23*323 + 4; hence not 23 divides 7433 by NAT_4:9;
    7433 = 29*256 + 9; hence not 29 divides 7433 by NAT_4:9;
    7433 = 31*239 + 24; hence not 31 divides 7433 by NAT_4:9;
    7433 = 37*200 + 33; hence not 37 divides 7433 by NAT_4:9;
    7433 = 41*181 + 12; hence not 41 divides 7433 by NAT_4:9;
    7433 = 43*172 + 37; hence not 43 divides 7433 by NAT_4:9;
    7433 = 47*158 + 7; hence not 47 divides 7433 by NAT_4:9;
    7433 = 53*140 + 13; hence not 53 divides 7433 by NAT_4:9;
    7433 = 59*125 + 58; hence not 59 divides 7433 by NAT_4:9;
    7433 = 61*121 + 52; hence not 61 divides 7433 by NAT_4:9;
    7433 = 67*110 + 63; hence not 67 divides 7433 by NAT_4:9;
    7433 = 71*104 + 49; hence not 71 divides 7433 by NAT_4:9;
    7433 = 73*101 + 60; hence not 73 divides 7433 by NAT_4:9;
    7433 = 79*94 + 7; hence not 79 divides 7433 by NAT_4:9;
    7433 = 83*89 + 46; hence not 83 divides 7433 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7433 & n is prime
  holds not n divides 7433 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
