A lower bound for the prime counting function
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Let π (x) count the primes p ≤ x, where x is a large real number. Euclid proved that there are infinitely many primes, so that π (x) → ∞ as x → ∞; in fact his famous argument ([1: Section 2.2]) can be used to show thatThere was no further progress on the problem of the distribution of primes until Euler developed various tools for the purpose; in particular he proved in 1737 [1: Theorem 427] that
1943 ◽
Vol 39
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pp. 1-21
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2011 ◽
Vol 54
(3)
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pp. 685-693
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1953 ◽
Vol 49
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pp. 59-62
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2011 ◽
Vol 32
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pp. 785-807
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1966 ◽
Vol 18
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pp. 1091-1094
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2014 ◽
Vol 24
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pp. 658-679
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2018 ◽
Vol 17
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pp. 127-151
1970 ◽
Vol 22
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pp. 569-581
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