The Quanta Podcast Mathematicians Discover Prime Conspiracy
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Mar 24, 2016 A surprising pattern in prime numbers: consecutive primes prefer certain final digits and avoid repeats. Reporters outline large-scale computations across different bases that reveal the effect. Experts explain why classic random models missed it and how the k-tuples conjecture predicts the bias. Reactions from number theorists and implications for teaching and future research are discussed.
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Unexpected Biases In Consecutive Primes
- Primes show surprising biases in the final digits of consecutive primes, preferring some endings and avoiding repeats.
- These biases persist far out along the number line and decay extremely slowly, contradicting naïve randomness assumptions.
Coin-Toss Paradox Sparked The Search
- Soundarajan heard a coin-tossing paradox and turned to primes, finding surprising digit preferences in base 3 then base 10.
- Lemke Oliver extended the search to the first 400 billion primes and confirmed the phenomenon.
Primes Repel Same Final Digits
- Primes ending in the same digit tend to repel each other, observed across bases and billions of primes.
- Numerical searches through vast primes confirmed the pattern, not explained by trivial spacing arguments.