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Not just winter.

Oaks produce huge numbers of acorns about one season every 7 years. My yard had thousands and thousands a few years ago, for example, but very few since. Oaks seem to do this to overwhelm squirrels and ensure that a few acorns manage to germinate. Squirrels that can save acorns for years will do much better than squirrels that can only save enough for each winter.

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Lots of tree species do this. They sync up and every few years overwhelm whatever eats their seeds.

So the same prey saturation strategy as cicadas? I wonder if that also produces a prime-number cycle preference

Phenological event known as "masting": https://en.m.wikipedia.org/wiki/Mast_(botany)

Similarly, periodical cicadas synchronously emerge in great numbers (more 370 per square meter) every 13th or 17th year.[1] This overwhelms predators and it's thought that the prime-numbered intervals prevent predators from synchronizing their reproductive cycles with that of the cicadas.

[1] https://en.wikipedia.org/wiki/Periodical_cicadas

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