
theorem
  4519 is prime
proof
  now
    4519 = 2*2259 + 1; hence not 2 divides 4519 by NAT_4:9;
    4519 = 3*1506 + 1; hence not 3 divides 4519 by NAT_4:9;
    4519 = 5*903 + 4; hence not 5 divides 4519 by NAT_4:9;
    4519 = 7*645 + 4; hence not 7 divides 4519 by NAT_4:9;
    4519 = 11*410 + 9; hence not 11 divides 4519 by NAT_4:9;
    4519 = 13*347 + 8; hence not 13 divides 4519 by NAT_4:9;
    4519 = 17*265 + 14; hence not 17 divides 4519 by NAT_4:9;
    4519 = 19*237 + 16; hence not 19 divides 4519 by NAT_4:9;
    4519 = 23*196 + 11; hence not 23 divides 4519 by NAT_4:9;
    4519 = 29*155 + 24; hence not 29 divides 4519 by NAT_4:9;
    4519 = 31*145 + 24; hence not 31 divides 4519 by NAT_4:9;
    4519 = 37*122 + 5; hence not 37 divides 4519 by NAT_4:9;
    4519 = 41*110 + 9; hence not 41 divides 4519 by NAT_4:9;
    4519 = 43*105 + 4; hence not 43 divides 4519 by NAT_4:9;
    4519 = 47*96 + 7; hence not 47 divides 4519 by NAT_4:9;
    4519 = 53*85 + 14; hence not 53 divides 4519 by NAT_4:9;
    4519 = 59*76 + 35; hence not 59 divides 4519 by NAT_4:9;
    4519 = 61*74 + 5; hence not 61 divides 4519 by NAT_4:9;
    4519 = 67*67 + 30; hence not 67 divides 4519 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4519 & n is prime
  holds not n divides 4519 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
