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The following is a list of foods that are allowed (legal) and foods that are not allowed (illegal) while following the Paleo diet. 

Palm oil Allowed Buy organic, unrefined.
Palm shortening Allowed
Papayas Allowed
Paprika Allowed Nightshade
Parsley Allowed
Parsnips Allowed
Passionfruit Allowed
Peaches Allowed Buy organic
Peanuts Not allowed Legume
Pears Allowed
Peas Not allowed
Pecans Allowed
Pepper, black Allowed Including whole peppercorns
Peppers Allowed Nightshade, buy organic
Peppermint Allowed
Persimmons Allowed
Pheasant Allowed
Pickles Allowed
Pineapples Allowed
Pine nuts Allowed
Pistachios Allowed
Plantains Allowed
Plums Allowed
Pomegranates Allowed
Pork Allowed
Potatoes Allowed if Primal Not allowed on whole30.
Prawns Allowed
Prunes Allowed
Pumpkin Allowed
Pumpkin pie spice Allowed
Pumpkin seeds Allowed
Purslane Allowed