I believe they used to test using rabbits - something to do with using their ovary and the cells would change if the test was positive. So obviously tests weren't common, not like you could pop down the chemists for a rabbit ovary!
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Its definately possible. With the right care provider.
I've heard of many babies being birthed at 43 weeks and some further along. Most of the stories I've read/heard of have been women with Midwives as care providers.
It obviously comes with some extra monitoring to make sure that all is ok with baby and the placenta.
I would imagine extremely prolonged pregnancies are more likely in times of war or famine, when there's a very good reason for the body to protect it's child by maintaining the pregnancy. But yes, I do believe that pregnancies, if left alone, could sometimes extend to more than one month over what we deem to be "normal".