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**11 - 15**of**15**### Different Approaches to the Distribution of Primes

- MILAN JOURNAL OF MATHEMATICS
, 2009

"... In this lecture celebrating the 150th anniversary of the seminal paper of Riemann, we discuss various approaches to interesting questions concerning the distribution of primes, including several that do not involve the Riemann zeta-function. ..."

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In this lecture celebrating the 150th anniversary of the seminal paper of Riemann, we discuss various approaches to interesting questions concerning the distribution of primes, including several that do not involve the Riemann zeta-function.

### On the irreducibility of a truncated binomial expansion

"... For positive integers k and n with k ≤ n − 1, define Pn,k(x) = k∑ ..."

### 1 On Goldbach’s Conjecture

, 2002

"... It is shown that if every odd integer n> 5 is the sum of three primes, then every even integer n> 2 is the sum of two primes. A conditional proof of Goldbach’s conjecture, based on Cramér’s conjecture, is presented. Theoretical and experimental results available on Goldbach’s conjecture allow that a ..."

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It is shown that if every odd integer n> 5 is the sum of three primes, then every even integer n> 2 is the sum of two primes. A conditional proof of Goldbach’s conjecture, based on Cramér’s conjecture, is presented. Theoretical and experimental results available on Goldbach’s conjecture allow that a less restrictive conjecture than Cramér’s conjecture be used in the conditional proof. A basic result of the Maier’s paper on Cramér’s model is criticized. 1

### First published online March 18, 2010 PRIME-REPRESENTING FUNCTIONS

"... Abstract. We construct prime-representing functions. In particular we show that there exist real numbers α> 1 such that ⌊ α 2n ⌋ is prime for all n ∈ N. Indeed the set consisting of such numbers α has the cardinality of the continuum. 1. ..."

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Abstract. We construct prime-representing functions. In particular we show that there exist real numbers α> 1 such that ⌊ α 2n ⌋ is prime for all n ∈ N. Indeed the set consisting of such numbers α has the cardinality of the continuum. 1.