# Longest repeated sequence in the prime counting function

## Main Question or Discussion Point

Is there a longest repeated sequence (congruency) in the prime counting function $$\pi (x)$$ (that which gives the number of primes less than or equal to x)?

Recall that $$\pi (x)$$, although infinite, may not be random, and itself starts out with an unrepeated sequence $$\pi (2)=1$$ and $$\pi (3)=2$$ (with a "slope" of 1).

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CRGreathouse
There are arbitrarily large gaps in the prime numbers. This means that $$\pi(n)$$ can be constant over an arbitrarily large interval.
Consider the n-1 numbers $$n!+k[/itex] where [itex]k=2,3,\cdots n$$