Seventy-one is prime and reduces to eight. Its firmest traditional use is Jewish institutional law: the Great Sanhedrin, the supreme court of ancient Israel, comprised seventy-one members, the seventy elders appointed to assist Moses, together with Moses himself as head, so that seventy-one is the number of the full high court, one more than the seventy of the elders. The odd number was deliberate, ensuring that the court could never be evenly split. Lesser courts were fixed at twenty-three, and the seventy-one of the Great Sanhedrin at the apex.
In chemistry, seventy-one is the atomic number of lutetium, named after Lutetia, the Latin name for Paris, the city of its discoverer Georges Urbain, and the last and heaviest of the lanthanide elements.
Seventy-one is prime, with no factors beyond one and itself. It is a twin prime, paired with 73, a prime just two away.
The genuine Pythagorean number philosophy that this modern chart borrows its name from left no writings of its own: Pythagoras and his early followers taught only by mouth, and what survives of their number theory comes instead through Nicomachus of Gerasa, whose Introduction to Arithmetic of the first century CE became the standard authority for a thousand years, and through Iamblichus, who drew on Nicomachus two centuries later; neither wrote anything resembling a name-and-birthdate numerology.