
theorem
  4513 is prime
proof
  now
    4513 = 2*2256 + 1; hence not 2 divides 4513 by NAT_4:9;
    4513 = 3*1504 + 1; hence not 3 divides 4513 by NAT_4:9;
    4513 = 5*902 + 3; hence not 5 divides 4513 by NAT_4:9;
    4513 = 7*644 + 5; hence not 7 divides 4513 by NAT_4:9;
    4513 = 11*410 + 3; hence not 11 divides 4513 by NAT_4:9;
    4513 = 13*347 + 2; hence not 13 divides 4513 by NAT_4:9;
    4513 = 17*265 + 8; hence not 17 divides 4513 by NAT_4:9;
    4513 = 19*237 + 10; hence not 19 divides 4513 by NAT_4:9;
    4513 = 23*196 + 5; hence not 23 divides 4513 by NAT_4:9;
    4513 = 29*155 + 18; hence not 29 divides 4513 by NAT_4:9;
    4513 = 31*145 + 18; hence not 31 divides 4513 by NAT_4:9;
    4513 = 37*121 + 36; hence not 37 divides 4513 by NAT_4:9;
    4513 = 41*110 + 3; hence not 41 divides 4513 by NAT_4:9;
    4513 = 43*104 + 41; hence not 43 divides 4513 by NAT_4:9;
    4513 = 47*96 + 1; hence not 47 divides 4513 by NAT_4:9;
    4513 = 53*85 + 8; hence not 53 divides 4513 by NAT_4:9;
    4513 = 59*76 + 29; hence not 59 divides 4513 by NAT_4:9;
    4513 = 61*73 + 60; hence not 61 divides 4513 by NAT_4:9;
    4513 = 67*67 + 24; hence not 67 divides 4513 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4513 & n is prime
  holds not n divides 4513 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
