06-27-2026, 07:36 PM
John Conway and his fruitful fractions
By David Benjamin
Summary
John Conway’s “fruitful fractions” are a beautiful example of how mathematics can hide surprising patterns inside simple ideas. Conway, one of the most creative mathematicians of the 20th century, designed a system of just 14 fractions that, when repeatedly multiplied in a specific way, can generate all prime numbers in order.
The process looks almost like a magic trick: starting from the number 2, the fractions create a sequence of integers, and whenever the result becomes a power of 2, its exponent is a prime number. Although this method is far too slow to compete with modern prime-search algorithms, it reveals Conway’s playful approach to mathematics—turning a simple set of fractions into a machine that explores the mysterious world of prime numbers.
ARTICLE
By David Benjamin
Summary
John Conway’s “fruitful fractions” are a beautiful example of how mathematics can hide surprising patterns inside simple ideas. Conway, one of the most creative mathematicians of the 20th century, designed a system of just 14 fractions that, when repeatedly multiplied in a specific way, can generate all prime numbers in order.
The process looks almost like a magic trick: starting from the number 2, the fractions create a sequence of integers, and whenever the result becomes a power of 2, its exponent is a prime number. Although this method is far too slow to compete with modern prime-search algorithms, it reveals Conway’s playful approach to mathematics—turning a simple set of fractions into a machine that explores the mysterious world of prime numbers.
ARTICLE
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