
theorem
  7331 is prime
proof
  now
    7331 = 2*3665 + 1; hence not 2 divides 7331 by NAT_4:9;
    7331 = 3*2443 + 2; hence not 3 divides 7331 by NAT_4:9;
    7331 = 5*1466 + 1; hence not 5 divides 7331 by NAT_4:9;
    7331 = 7*1047 + 2; hence not 7 divides 7331 by NAT_4:9;
    7331 = 11*666 + 5; hence not 11 divides 7331 by NAT_4:9;
    7331 = 13*563 + 12; hence not 13 divides 7331 by NAT_4:9;
    7331 = 17*431 + 4; hence not 17 divides 7331 by NAT_4:9;
    7331 = 19*385 + 16; hence not 19 divides 7331 by NAT_4:9;
    7331 = 23*318 + 17; hence not 23 divides 7331 by NAT_4:9;
    7331 = 29*252 + 23; hence not 29 divides 7331 by NAT_4:9;
    7331 = 31*236 + 15; hence not 31 divides 7331 by NAT_4:9;
    7331 = 37*198 + 5; hence not 37 divides 7331 by NAT_4:9;
    7331 = 41*178 + 33; hence not 41 divides 7331 by NAT_4:9;
    7331 = 43*170 + 21; hence not 43 divides 7331 by NAT_4:9;
    7331 = 47*155 + 46; hence not 47 divides 7331 by NAT_4:9;
    7331 = 53*138 + 17; hence not 53 divides 7331 by NAT_4:9;
    7331 = 59*124 + 15; hence not 59 divides 7331 by NAT_4:9;
    7331 = 61*120 + 11; hence not 61 divides 7331 by NAT_4:9;
    7331 = 67*109 + 28; hence not 67 divides 7331 by NAT_4:9;
    7331 = 71*103 + 18; hence not 71 divides 7331 by NAT_4:9;
    7331 = 73*100 + 31; hence not 73 divides 7331 by NAT_4:9;
    7331 = 79*92 + 63; hence not 79 divides 7331 by NAT_4:9;
    7331 = 83*88 + 27; hence not 83 divides 7331 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7331 & n is prime
  holds not n divides 7331 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
