SOLUTION: "I'm a product of four prime numbers. My three digits are all prime and different. The sum of my prime factors is 30. What number am I?

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Question 258335: "I'm a product of four prime numbers. My three digits are all prime and different. The sum of my prime factors is 30. What number am I?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

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, not necessarily all different.
My three digits are all prime and different. The sum of those four primes,
not necessarily all different, of which I am the product 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

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