Question 258335
<pre><font size = 4 color ="indigo"><b>
This problem is slightly misstated.  If taken literally, there is no integer
satisfying all those properties.  The property "The sum of my prime factors is
30", if taken literally, allows no solution.  

However it would have a solution:

"I'm a product of four prime numbers<font color = "red">, not necessarily all different</font>.
My three digits are all prime and different. The sum of <font color = "red">those four primes,
not necessarily all different, of which I am the product</font> is 30. What number
am I?"

Stated that way there is a solution, 532, For 532 has 3 prime digits, all
different and it is the product of 4 prime factors, since 2x2x7x19=532,
and the sum of those four numbers, using 2 twice(!) is 2+2+7+19=30.

However, literally speaking, it has only 3 prime factors 2,7, and 19,
and their sum is not 30, but only 28.  The author of this problem
is counting the prime factor which it contains twice, as two
prime factors.

Edwin</pre>