New Scientist’s Brain Twister 7: Home Primes
<p>home prime of a number, follow this procedure: first, find its prime factors; then concatenate these by writing the prime factors in size order to form a new number using all of their digits; then repeat until the resulting number is prime.</p>
<p>For example, 9 = 3 × 3, so its prime factors are 3 and 3. These concatenate to give 33. Now, find the prime factors of 33. They are 3 and 11, which concatenate to give 311. Since 311 is prime, we stop and say that the home prime of 9 is 311.</p>
<p>The home prime of a prime number is the number itself. So, for example, the home prime of 2 is 2.</p>
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