I will be doing some research on Home Primes and the lack of resources online baffled me. I would be grateful and thankful to those who contribute to this post adding their prior knowledge , links, facts and information about Home Primes.
I can then also add these information to the common sites such as wolfram and wikipedia to make others access knowledge quicker.
Also if anyone knows, why is there a huge mystery and vagueness in the research of home primes?
For anyone who does not know what a Home Prime is:
A Home Prime is the terminating prime in a sequence in concatenating the prime divisors of a number.
This may sound very abstract but an example will do
lets take 49
49 = 7x7 therefore we write it as 77
77 = 7x11 therefore we write it as 711
and we continue until we find a prime
since if we hit a prime we cannot factorise it any longer, the sequence ends and that prime is called a home prime.
Just my opinion, but Home Primes started out as recreational math. But you'll find there's likely no known shortcut for calculating what it will be from the start number. Thus it relies on the toughness of factoring. You can get a few hints about factors by modular arithmetic, but it's not really that much help ... attempting to work backwards doesn't help much more ...