Prime Factor Sequences
Start with any integer n. Add n to its own prime factors. If the sum is a prime number, the sequence terminates. If not, repeat the process until it does. I call this a PFS - a Prime Factor Sequence.
Note: an integer's prime factors are all the least prime numbers whose product equals the integer.
Example: 24, 33, 47. This is a PFS of three terms. 24 plus its prime factors is 33; 33 plus its prime factors is 47, and 47 is a prime number.
What is the longest PFS with a first term under 1,000?