
theorem
  617 is prime
proof
  now
    617 = 2*308 + 1; hence not 2 divides 617 by NAT_4:9;
    617 = 3*205 + 2; hence not 3 divides 617 by NAT_4:9;
    617 = 5*123 + 2; hence not 5 divides 617 by NAT_4:9;
    617 = 7*88 + 1; hence not 7 divides 617 by NAT_4:9;
    617 = 11*56 + 1; hence not 11 divides 617 by NAT_4:9;
    617 = 13*47 + 6; hence not 13 divides 617 by NAT_4:9;
    617 = 17*36 + 5; hence not 17 divides 617 by NAT_4:9;
    617 = 19*32 + 9; hence not 19 divides 617 by NAT_4:9;
    617 = 23*26 + 19; hence not 23 divides 617 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 617 & n is prime
  holds not n divides 617 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
