The first 50 million prime numbers

  title={The first 50 million prime numbers},
  author={D. Zagier},
  journal={The Mathematical Intelligencer},
  • D. Zagier
  • Published 1977
  • The Mathematical Intelligencer
Optimal limits for π ( n ) using Zagier ’ s method
Zagier [4] showed using elementary methods that π(n), the number of primes less than or equal to n, can be bounded by 2 3 n logn < π(n) < 1.7 n logn . His proof, which used strong induction andExpand
Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology
It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. InExpand
Dynamic Processes of Formation Classes of Prime Numbers in a Probabilistic Model of Mathematical Computer Proof of the Generalized Artin Hypothesis
  • G. Vostrov, R. Opiata
  • Mathematics
  • 2019 XIth International Scientific and Practical Conference on Electronics and Information Technologies (ELIT)
  • 2019
The analysis of the probabilistic approach to solving the problem of the distribution of primes in the generalized Artin's hypothesis is given. The foundations of a computer approach to solvingExpand
Defining the prime numbers prior to the integers: A first-principles approach to the distribution of primes
While the prime numbers have been subject to mathematical inquiry since the ancient Greeks, the accumulated effort of understanding these numbers has - as Marcus du Sautoy recently phrased it - 'notExpand
Matrix model for Riemann zeta via its local factors
We propose the construction of an ensemble of unitary random matrices (UMM) for the Riemann zeta function. Our approach to this problem is `$p$-iecemeal', in the sense that we consider each factor inExpand
Some heuristics on the gaps between consecutive primes
We give a review of the rigorous results on the gaps between consecutive primes. Next we present heuristic arguments leading to the formula for the number of pairs of consecutive primes pn, pn+1 < xExpand
Infinite Number of Twin Primes
This work is devoted to the theory of prime numbers. Firstly it introduced the concept of matrix primes, which can help to generate a sequence of prime numbers. Then it proposed a number of theorems,Expand
On the Location of the Non-Trivial Zeros of the RH via Extended Analytic Continuation
This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.
This study is aimed at adapting recent methods for generating large random primes such as needed in public-key cryptosystems, and an algorithm has been implemented. Expand
La lezione mancata
Facciamo una breve panoramica dei più importanti risultati sulla distribuzione dei numeri primi. Andremo sostanzialmente in ordine cronologico presentando i risultati dei matematici più importantiExpand