Home primes: Difference between revisions

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In number theory, the '''home prime HP(n)''' of an integer '''n''' greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions.

The traditional notation has the prefix "HP" and a postfix count of the number of iterations until the Home prime is found (if the count is greater than 0), for instance HP4(2) === HP22(1) === 211 is the same as saying home_prime(4) needs 2 iterations and is the same as home_prime(22) which needs 1 iteration, and (both) ~~equal~~ 211, a prime.

The traditional notation has the prefix "HP" and a postfix count of the number of iterations until the Home prime is found (if the count is greater than 0), for instance HP4(2) === HP22(1) === 211 is the same as saying home_prime(4) needs 2 iterations and is the same as home_prime(22) which needs 1 iteration, and (both) resolve to 211, a prime.

Prime numbers are their own Home prime;

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;Task

Find and show here, on this page, the Home prime iteration chains for the integers 2 through 20 inclusive.

* Find and show here, on this page, the Home prime iteration chains for the integers 2 through 20 inclusive.

;Stretch goal

Find and show the iteration chain for 65.

* Find and show the iteration chain for 65.

;Impossible goal

Show the the Home prime for HP49.

* Show the the Home prime for HP49.

;See also

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;* [[oeis:A037274|OEIS:A037274 - Home primes for n >= 2]]

;* [[oeis:A056938|OEIS:A056938 - Concatenation chain for HP49]]

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=={{header|Factor}}==