Although the first step to living a Paleo lifestyle is to consume lots of plants, mostly we mean vegetables and some of the lower-carb fruits such as tomatoes, peppers, and cucumbers. The sweeter fruits can absolutely be included as part of a healthy Paleo lifestyle, just remember to moderate your consumption.
The Nutrient Content of Plums
Plums are fairly high in carbohydrates, and most of those carbs are straight sugar, with only a nominal amount of dietary fiber. They are a good source of vitamin C, but contain only small amounts of other nutrients, such as B vitamins, magnesium, phosphorous, and potassium. They are high in antioxidants, though, which are necessary for maintaining a healthy immune system and protecting against chronic conditions such as diabetes and heart disease.
Mark Sisson listed plums and prunes among the fruits with the most antioxidants in this post.
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As far as whether the carbohydrate content of plums will have a negative or positive effect on your health goals, that is entirely individual. Some people find that they thrive on a diet that is extremely low in carbohydrates, while others find that they require a slightly higher carbohydrate content. This can depend on factors such as your activity level, but the bottom line is that self-experimentation is the only way to know what works best for you. Play around with your carbohydrate content and see what makes you feel your best.