## How Many Primes up to BillionXTrillion? Approximating the Riemann Hypothesis Series

### H. Vic Dannon

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How many prime numbers up to 10? 2, 3, 5, and 7 are the four prime numbers up to 10. Lehmer have listed the prime numbers up to 10,006,721, and we can count with his list. A supercomputer was used to count how many primes are up to a Billion times a Trillion. But isn't there some formula to replace counting? In 1859 Riemann derived -assuming the Riemann Hypothesis- the Formula for the Count of the Primes up to a given number. The Riemann Hypothesis enables us to compute an infinite series in the formula, at the infinitely many zeros of the Riemann Zeta function on the line 1/2+iy. The Riemann Hypothesis Series can only be approximated by its partial sums, which converge unpredictably. The approximation of the Hypothesis Series, and of the Count of the Primes up to a number, may improve by the use of many zeta zeros. We use Riemann's Formula to approximate the number of Primes up to a (Billion)x(Trillion)=10^21.

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## 1.How Many Primes up to BillionXTrillion? Approximating the Riemann Hypothesis Series

ISBN 10: 0980128730 ISBN 13: 9780980128734
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Book Description Gauge-Institute, 2008. Paperback. Book Condition: Used: Good. 1ST. Bookseller Inventory # SONG0980128730