Why is my iPhone 4 always shutting itself off when not on charge?

Today I got a new iPhone 4 and for the first hour or so it was working fine. It kept turning itself off whenever it wasn't on the charger but it was already fully charged. I would turn it on then it would just turn straight off. I need help.

Oh Amy sister what you did, you bought new iPhone 4, you know apple has discontinued 4, 4s, 5?

It is very old phone

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