Some natural numbers can be expressed as a sum of consecutive natural numbers in more than one way. For example, $7$ can get expressed both as $7$, and $(3+4).$ In terms of a sum of consecutive numbers, $4$ and $8$ can only get expressed as $4$, and $8$ respectively. Call such numbers consecutive-primes. How many consecutive-primes exist? Given all previous consecutive-primes, is there a way to compute the next consecutive-prime?
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