Time between New job, how to handle it

So i have just recently accepted a new position at a fairly large company. It is a junior level position that pays pretty well.

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So, I don't actually start until May 13th. I gave my notice last week after clearing the background check (thankfully) and will work at my current job until May 1st. I feel like this is a long time between jobs, do i need to reach out to the people ill be working with in the interim? I have just been in contact with the HR onboarding person at this point getting paperwork e-signed.

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Because of how much time there is until the start date i am unsure of what to do in the interim. Anyone ever run across the same sort of issue or is it just me?

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