Ononot — The 'Heath-Brown's Theorem' (1984) on prime gaps states that

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Primeshard

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The 'Heath-Brown's Theorem' (1984) on prime gaps states that there are infinitely many $n$ such that $p_{n+1} - p_n < \ln p_n$ . What is the constant factor for the logarithmic gap in the best version of this theorem?