Small Gaps Between Primes

paper by Goldston and Yildirim

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July 20, 2026

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The paper "Small Gaps Between Primes" by Daniel Goldston and Cem Yildirim, along with later work by J\u00e1nos Pintz, established that there are infinitely many pairs of primes that differ by a small, finite amount. This built upon the twin prime conjecture, which posits that there are infinitely many prime pairs with a difference of 2. While Goldston and Yildirim's initial proof had a flaw, it was corrected, and subsequent work by Yitang Zhang and others has progressively reduced the maximum gap between such prime pairs. Primes are integers greater than 1 divisible only by themselves and 1.12

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twin prime conjecture
…Yildirim published a paper, “Small Gaps Between Primes,” that established the existence of an infinite number of prime pairs within a small difference (16, with certain other assumptions, most notably that of the Elliott-Halberstam conjecture). Although their proof was flawed, they corrected it with Hungarian mathematician János Pintz in…
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…Yildirim published a paper, “Small Gaps Between Primes,” that established the existence of an infinite number of prime pairs within a small difference (16, with certain other assumptions, most notably that of the Elliott-Halberstam conjecture). Although their proof was flawed, they corrected it with Hungarian mathematician János Pintz in…
Read More