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The normal distribution of the prime factors
Sieving by an interval
7 other sections not shown
according appears apply assume asymptotic density average begin Chapter completes condition conjecture consider constant continuous counted deduce define definition denote depends distribution function divisors employ equal Erdős error term establish estimate example exceed Exercise exists exponent fact fixed follows formula function given gives Hall Hence holds idea implies increasing induction inequality integers interval introduce involving least Lemma log x log2 logarithmic lower bound main term means method moreover normal order Notes notice obtain partial positive possible precisely prime factors problem Proof of Theorem prove question range replaced restricted result right-hand side satisfies sequence similar simple squarefree sufficient suitable summation suppose Tenenbaum term Theorem 01 theory uniformly upper bound whence write x(log yields