Question

PLEASE HELP!!!!! And explain too! Thanks!!!

I am a prime number between 40 & 50. If you add one to me, the sum of ALL prime factors of that composite number is 15. What number am I?

Answer 1

I don't know any slick way to do this. I would just list the prime numbers
between 40 and 50 and test them one at a time.

The prime numbers between 40 and 50 are: 41, 43, 47

Test 41:
-- add 1 . . . 42
-- prime factors of 42 . . . 2, 3, 7
-- sum of the factors . . . 12

Test 43:
-- add 1 . . . 44
-- prime factors of 44 . . . 2, 11
-- sum of the factors . . . 13

Test 47:
-- add 1 . . . 48
-- prime factors of 48 . . . 2, 3,
-- sum of the factors . . . 5

Maybe I'm not understanding how to list prime factors, but so far,
I haven't found any number that answers the question.

Maybe if I write the prime factorization of 44 like this:

44 = 2 * 2 * 11

Now the items in the prime factorization do add up to 15.
So the answer would seem to be 43.