Unique Length Jumps and Constant Zero Intervals in Prime Number Representations in Base 7

In the base 7 representations of prime numbers, the lengths of their digit expansions exhibit a striking dichotomy: they remain constant (interval 0) for most consecutive primes, and increase by exactly one digit only at specific primes crossing powers of 7. These +1 jumps occur with a mean frequency of approximately 1/56, and the normalized gaps between these primes include cyclic fractions of 1/7. This structure, unique to base 7 and absent in other bases, may represent a novel contribution to number theory.