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We describe a rigorous implementation of the Lagarias and Odlyzko Analytic Method to evaluate the prime counting function and its use to compute unconditionally the number of primes less than $10^{24}$.
B. Rosser, Explicit bounds for some functions of prime numbers , Amer. J. Math. 63
1941
Earlier work this paper cites.
D.H. Lehmer, On the exact number of primes less than a given limit , Illinois J. Math. 3
1959
Earlier work this paper cites.
R.E. Moore, Interval analysis , vol. 60, Prentice-Hall Englewood Cliffs, New Jersey, 1966
1966
Earlier work this paper cites.
Tom M. Apostol, Introduction to Analytic Number Theory , Undergraduate Texts in Mathematics, Springer, 1976
1976
Earlier work this paper cites.
J.C. Lagarias, V.S. Miller, and A.M. Odlyzko, Computing π ( x ) \pi(x) : the Meissel-Lehmer method , Math. Comp. 44
1985
Earlier work this paper cites.
J. C. Lagarias and A. M. Odlyzko, Computing π ( x ) \pi(x) : an Analytic Method , J. Algorithms 8
1987
Cited alongside, same era.
The Course Team, Complex Analysis Handbook , The Open University, 1994
1994
Cited alongside, same era.
M. Deléglise and J. Rivat, Computing π ( x ) \pi(x) : the Meissel, Lehmer, Lagarias, Miller, Odlyzko method , Math. Comp. 65
1996
Cited alongside, same era.
H. Davenport, Multiplicative Number Theory , third ed., Graduate Texts in Mathematics, no. 74, Springer, 2000
2000
Cited alongside, same era.
N. Revol and F. Rouillier, A library for arbitrary precision interval arithmetic , 10th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics, 2002
2002
Cited alongside, same era.
J. Büthe, J. Franke, A. Jost, and T. Kleinjung, A practical analytic method for calculating π ( x ) \pi(x) , to appear
Cited in the paper.
D.F.E. Meissel, Über die Bestimmung der Primzahlenmenge innerhalb gegebener Grenzen , Math. Ann. 2
Cited in the paper.
by same author, Berechnung der Menge von Primzahlen, welche innerhalb der ersten Milliarde natürlicher Zahlen vorkommen , Math. Ann. 25
Cited in the paper.
A.O.L. Atkin and D.J. Bernstein, Prime sieves using binary quadratic forms , Math. Comp. 73
2004
Later among the works it cites.
W.F. Galway, Analytic Computation of the Prime Counting Function , Ph.D. thesis, University of Illinois at Urbana-Champaign, 2004
2004
Later among the works it cites.
Andrew R. Booker, Artin’s conjecture, Turing’s method and the Riemann hypothesis , Experiment. Math. 15
2006
Later among the works it cites.
Jonathan Bober, Database of zeros of the zeta function , 2012, http://sage.math.washington. edu/home/bober/www/data/platt_zeros/zeros
2012
Closest in time.
David J. Platt, Computing ζ \zeta on the half line , In preparation (2013)
2013
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