This number is a prime.
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55555544444441 is the smallest prime that produces a chain of 5 primes applying the following rule to each prime of the chain: Sum every digit powered to itself. E.g., 55555544444441 -> 20543 -> 3413 -> 311 -> 29. A chain of 6 provable primes will not be established for a long, long time. [Rivera]