People can disagree as to what our natural rights are. Perhaps the most famous listing of our natural rights comes from the Declaration of Independence of the United States. In that document, Thomas Jefferson said that among our natural rights were life, liberty, and the pursuit of happiness. When he wrote that, he was borrowing from John Locke, who said that our natural rights were the right to life, liberty and property.
This is a pretty good summation of people's natural rights. We have the right to live (not to be killed by another person) the right to our liberty (not to be enslaved or otherwise controlled by others) and the right to property (the right not to have our things taken from us by force).
One person's views on this issue may differ widely from another's views, but we might all agree that individuals have a right to safety and to the pursuit of a livelihood. Without these rights, we cannot live peacefully.
This falls short of being translatable to a right to prosperity. Rights to safety and to the pursuit of a livelihood form a basic coupling of rights to life; to autonomous life.