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PUZZLET 217

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?




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Last Updated: May 27th, 2010.