
theorem
  4517 is prime
proof
  now
    4517 = 2*2258 + 1; hence not 2 divides 4517 by NAT_4:9;
    4517 = 3*1505 + 2; hence not 3 divides 4517 by NAT_4:9;
    4517 = 5*903 + 2; hence not 5 divides 4517 by NAT_4:9;
    4517 = 7*645 + 2; hence not 7 divides 4517 by NAT_4:9;
    4517 = 11*410 + 7; hence not 11 divides 4517 by NAT_4:9;
    4517 = 13*347 + 6; hence not 13 divides 4517 by NAT_4:9;
    4517 = 17*265 + 12; hence not 17 divides 4517 by NAT_4:9;
    4517 = 19*237 + 14; hence not 19 divides 4517 by NAT_4:9;
    4517 = 23*196 + 9; hence not 23 divides 4517 by NAT_4:9;
    4517 = 29*155 + 22; hence not 29 divides 4517 by NAT_4:9;
    4517 = 31*145 + 22; hence not 31 divides 4517 by NAT_4:9;
    4517 = 37*122 + 3; hence not 37 divides 4517 by NAT_4:9;
    4517 = 41*110 + 7; hence not 41 divides 4517 by NAT_4:9;
    4517 = 43*105 + 2; hence not 43 divides 4517 by NAT_4:9;
    4517 = 47*96 + 5; hence not 47 divides 4517 by NAT_4:9;
    4517 = 53*85 + 12; hence not 53 divides 4517 by NAT_4:9;
    4517 = 59*76 + 33; hence not 59 divides 4517 by NAT_4:9;
    4517 = 61*74 + 3; hence not 61 divides 4517 by NAT_4:9;
    4517 = 67*67 + 28; hence not 67 divides 4517 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4517 & n is prime
  holds not n divides 4517 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
