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According to Wolfram Alpha and the tables in [2], 2], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper we find that $\pi(10^{10}) = 455, 052, 512$.
Wonder whether someone has already noted this discrepancy between the sources elsewhere. Naturally, the discrepancy implies the existence of a bug in either the routines of Zagier or in WA's implementation of the prime counting function. I don't think that it's only a typo in Zagier' note because, if memory serves me right, there are some other texts in the literature that endorse the computations of Zagier (for instance, see [1, page 7.)7].).
References
[1] 1] A. E. Ingham. The distribution of prime numbers. Cambridge Mathematical Library.
[2] 2] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, 1994, Birkhäuser.
[3] 3] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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edited Sep 16 2010 at 2:25 |
According to Wolfram Alpha and the tables in [1], 2], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper we find that $\pi(10^{10}) = 455, 052, 512$.
Wonder whether someone has already noted this discrepancy between the sources elsewhere. Naturally, the discrepancy implies the existence of a bug in either the routines of Zagier or in WA's implementation of the prime counting function. I don't think that it's only a typo in Zagier' note because, if memory serves me right, there are some other texts in the literature that endorse the computations of Zagier (for instance, see 1, page 7.).
References
[1] A. E. Ingham. The distribution of prime numbers. Cambridge Mathematical Library.
[2] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, 1994, Birkhäuser.
[2] 3] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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edited Sep 16 2010 at 2:15 |
According to Wolfram Alpha and the tables in [1], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper we find that $\pi(10^{10}) = 455, 052, 512$.
Wonder whether someone has already noted this discrepancy between the sources elsewhere. Naturally, the discrepancy implies the existence of a bug in either the routines of Zagier or in WA's implementation of the prime counting function. I don't think that it's only a typo in Zagier' note because, if memory serves me right, there are some other texts in the literature that endorse the computations of Zagier.
References
[1] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, 1994, Birkhäuser.
[2] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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edited Sep 16 2010 at 1:57 |
According to Wolfram Alpha and the tables in [1], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper we find that $\pi(10^{10}) = 455, 052, 512$.
Wonder whether someone had has already noted this discrepancy between the sources elsewhere.
References
[1] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, 1994, Birkhäuser.
[2] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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edited Sep 16 2010 at 1:51 |
According to Wolfram Alpha and the tables in [1], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper we find that $\pi(10^{10}) = 455, 052, 512$.
Wonder whether someone here had already noted this discrepancy between the sources.
References
[1] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, Birkhäuser.
[2] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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edited Sep 16 2010 at 1:44 |
According to Wolfram Alpha and the tables in [1], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper (see [2]) we find that $\pi(10^{10}) = 455, 052, 512$. Whichever the right number turns out to be, it has always been it...
Wonder whether someone here had already noted this discrepancy between the sources.
References
[1] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, Birkhäuser.
[2] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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answered Sep 16 2010 at 1:38 |
According to Wolfram Alpha and the tables in [1], $\pi(10^{10}) = 455, 052, 511$. Nevertheless, in Zagier's paper (see [2]) we find that $\pi(10^{10}) = 455, 052, 512$. Whichever the right number turns out to be, it has always been it...
Wonder whether someone here had already noted this discrepancy between the sources.
References
[1] H. Riesel. Prime Numbers and Computer Methods for Factorization. Second Edition, Birkhäuser.
[2] D. Zagier. "The first 50 million primes". Math. Intelligencer, 0 (1977).
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