I was surprised to find that the number associated with my diurnal age today, 27525, is a number for which a home prime is not able to be ascertained. See Figure 1 where the algorithm applied to this number quits after 50 concatenations fail to generate a prime.
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Figure 1: permalink |
However, what surprised me even further was that the very next number, 27526, is also a number for which a home prime is not able to be ascertained. Such pairs are not unprecedented, the first being 714 and 715 followed by 1138 and 1139. See my blog post Home Primes from 2nd May 2021. The very first number for which a home prime cannot be found is 49.
After 27526, the next number 27527 is prime and I've written about this number in a post What's Special About 27527 on 10th August 2024. After that, 27528 requires ten steps and 27529 is a prime. I'll continue to monitor the home primes for forthcoming numbers. There's no way of knowing whether these numbers for which home primes are currently unobtainable will not eventually be found to reach home primes once quantum computers are focused on the problem.
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