7 added 22 characters in body

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).

6 added 127 characters in body; deleted 2 characters in body

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).

5 added 329 characters in body; deleted 2 characters in body

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).

4 added 16 characters in body
3 deleted 5 characters in body
2 deleted 12 characters in body; deleted 69 characters in body
1