
theorem
  4663 is prime
proof
  now
    4663 = 2*2331 + 1; hence not 2 divides 4663 by NAT_4:9;
    4663 = 3*1554 + 1; hence not 3 divides 4663 by NAT_4:9;
    4663 = 5*932 + 3; hence not 5 divides 4663 by NAT_4:9;
    4663 = 7*666 + 1; hence not 7 divides 4663 by NAT_4:9;
    4663 = 11*423 + 10; hence not 11 divides 4663 by NAT_4:9;
    4663 = 13*358 + 9; hence not 13 divides 4663 by NAT_4:9;
    4663 = 17*274 + 5; hence not 17 divides 4663 by NAT_4:9;
    4663 = 19*245 + 8; hence not 19 divides 4663 by NAT_4:9;
    4663 = 23*202 + 17; hence not 23 divides 4663 by NAT_4:9;
    4663 = 29*160 + 23; hence not 29 divides 4663 by NAT_4:9;
    4663 = 31*150 + 13; hence not 31 divides 4663 by NAT_4:9;
    4663 = 37*126 + 1; hence not 37 divides 4663 by NAT_4:9;
    4663 = 41*113 + 30; hence not 41 divides 4663 by NAT_4:9;
    4663 = 43*108 + 19; hence not 43 divides 4663 by NAT_4:9;
    4663 = 47*99 + 10; hence not 47 divides 4663 by NAT_4:9;
    4663 = 53*87 + 52; hence not 53 divides 4663 by NAT_4:9;
    4663 = 59*79 + 2; hence not 59 divides 4663 by NAT_4:9;
    4663 = 61*76 + 27; hence not 61 divides 4663 by NAT_4:9;
    4663 = 67*69 + 40; hence not 67 divides 4663 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4663 & n is prime
  holds not n divides 4663 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
