## 2006.94: A new bound for the smallest x with \pi(x) > \li(x)

2006.94:
Kuok Fai Chao and Roger Plymen
(2006)
*A new bound for the smallest x with \pi(x) > \li(x).*
math.NT/0509312.
pp. 1-16.

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Official URL: http://arxiv.org/abs/math.NT/0509312

## Abstract

We reduce the dominant term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays & Hudson. Entering 2,000,000 Riemann zeros, we prove that there exists x in the interval [1.39792101 \times 10^316, 1.39847603 \times 10^316] for which \pi(x) > \li(x). This interval is strictly a sub-interval of the interval in Bays & Hudson [1], and is narrower by a factor of about 10.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Number of primes up to x. Logarithmic integral. Riemann zeros. A bound for the first crossover. |

Subjects: | MSC 2000 > 11 Number theory |

MIMS number: | 2006.94 |

Deposited By: | Professor Roger Plymen |

Deposited On: | 17 May 2006 |

### Available Versions of this Item

- A new bound for the smallest x with \pi(x) > \li(x) (deposited 23 February 2010)
- A new bound for the smallest x with \pi(x) > \li(x) (deposited 17 May 2006)
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- A new bound for the smallest x with \pi(x) > \li(x) (deposited 17 May 2006)

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