There is no link between prime numbers and crickets in general.
There are one or two special types of cricket that wait a number of years to mate, in order to escape the attentions of a deadly predator. The number of years is prime because that minimises the chances of a coincidental meeting with the predators.
The classic example is a locust which has a seventeen year mating cycle.
ps the predator has not been found; it is probably extinct now.
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