
theorem
  613 is prime
proof
  now
    613 = 2*306 + 1; hence not 2 divides 613 by NAT_4:9;
    613 = 3*204 + 1; hence not 3 divides 613 by NAT_4:9;
    613 = 5*122 + 3; hence not 5 divides 613 by NAT_4:9;
    613 = 7*87 + 4; hence not 7 divides 613 by NAT_4:9;
    613 = 11*55 + 8; hence not 11 divides 613 by NAT_4:9;
    613 = 13*47 + 2; hence not 13 divides 613 by NAT_4:9;
    613 = 17*36 + 1; hence not 17 divides 613 by NAT_4:9;
    613 = 19*32 + 5; hence not 19 divides 613 by NAT_4:9;
    613 = 23*26 + 15; hence not 23 divides 613 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 613 & n is prime
  holds not n divides 613 by XPRIMET1:18;
  hence thesis by NAT_4:14;
