[seqfan] Re: Do 20 and 105 eventually reach a prime in these sequences?

[franktaw at netscape.net]

Most *small* integers quickly reach a prime.  I'm confident that most 
integers do not.

Franklin T. Adams-Watters

-----Original Message-----
From: Alonso Del Arte <alonso.delarte at gmail.com>

...
If we take the factorization of an integer, say 18 = 2 * 3^2, strip out 
the
operators and concatenate the integers, then repeat the operation, most
integers quickly reach a prime. Indeed, 232 = 2^3 * 29, and 2329 = 17 * 
137,
and 17137 is prime.

...

Do 20 and 105 reach a prime under this process? With 20 we get 20, 225,
3252, 223271, 297699, 399233, 715623, 3263907, 32347303, ... I've taken 
this
to forty steps, and 4339779194757514315803243245042123341102411963 is
composite. Similary with 105: 105, 357, 3717, 32759, 174147, 358049, 
379677,
3196661, 13245897, ... and at forty steps,
7903796151050019316957414263672508157280737 is composite.