Take a natural number's prime factors and list them increasingly and repeating them according to multiplicity. Concatenate their decimal (or in any base) representation to get a new number and repeat the process. Does this always end in a prime number for any input? 



Does listing the prime factors always stop?
It's open problem, sequence [A037274](http://www.research.att.com/~njas/sequences/A037274) from OEIS, so-called "[home primes](http://mathworld.wolfram.com/HomePrime.html)". Hm, the value for n=77 is even unknown.


P.S. [On-Line Encyclopedia of Integer Sequences](http://www.research.att.com/~njas/sequences/) definitely should be included in FAQ.


