1953 Turing


Father (Mother) of modern computer science. Did many amazing things.

Including work on "non-computable" numbers an example of which I can not provide.

In relation to Riemann zeros, computed and confirmed that the first 1,104 zeros were on the critical line based on the Riemann-Siegel formula.

Numerical computations have been made threw the ages to check the RH on the first zeros. Computer age, starting with Turing computations, permitted verification to more than  a billions zeros.

A history of the RH verification on the first n zeros is given below.
Year n Author
1903 15 J. P. Gram 
1914 79 R. J. Backlund 
1925 138 J. I. Hutchinson 
1935 1,041 E. C. Titchmarsh 
1953 1,104 A. M. Turing 
1956 15,000 D. H. Lehmer 
1956 25,000 D. H. Lehmer 
1958 35,337 N. A. Meller 
1966 250,000 R. S. Lehman 
1968 3,500,000 J. B. Rosser, J. M. Yohe, L. Schoenfeld 
1977 40,000,000 R. P. Brent 
1979 81,000,001 R. P. Brent
1982 200,000,001 R. P. Brent, J. van de Lune, H. J. J. te Riele, D. T. Winter 
1983 300,000,001 J. van de Lune, H. J. J. te Riele
1986 1,500,000,001 J. van de Lune, H. J. J. te Riele, D. T. Winter 
2001 10,000,000,000 J. van de Lune 
2004 900,000,000,000 S. Wedeniwski 
2004 10,000,000,000,000 X. Gourdon and Patrick Demichel 
The latest RH verification on the first 1013 zeros have been achieved thanks to the use of the fast Zeta evaluation algorithm by Odlyzko and Schönhage, and that it is the first RH verification done with this technique.

Turing sadly took his own life in 1954.

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