On the order of the non-primes of type 6n+5 and 6n+1

The fundamental importance of prime numbers for mathematics is that all other natural numbers can be represented as a unique product of prime numbers[1]. For centuries, mathematicians have been trying to find an order in the occurrence of prime numbers. Since Riemann´s paper on the number of primes under a given size, the distribution of the primes is assumed to be random[2]. Here, I show that prime numbers are not randomly distributed using three parametric sine functions. Their positions are determined by the order of occurrence of the nonprimes of types 6n+5 and 6n+1. Furthermore, I will show an exact primality test using these three parametric sine functions.

PELATIHAN KONSEP PEMASARAN DALAM RANGKA OPTIMALISASI PEMASARAN PRODUK KHAS TAMIYANG

Community service is one of the three principles of higher education that has an impact on improving the quality of the people it serves. Maranatha Christian University is one of the universities that seeks to be able to provide the widest possible way to improve the quality of society in community service activities. We lecturers of Entrepreneurshipand Marketing Major as part of Maranatha Christian University make this happen through community service activities at GKP Tamiyang Indramayu. The community service activities discuss the marketing conceptdan its implication towards marketing of Tamiyang's unique products. The method of implementing PKM activities is carried out by training, in the form of exposure to marketing concepts and several things that can be applied in marketing of Tamiyang’s unique product. With this marketing concept training, it is hoped that they can find market potential and increase the knowledge of potential consumers on Tamiyang's unique products, so that it can become a strategy in marketing optimization of Tamiyang's unique products. Pengabdian kepada masyarakat adalah salah satu tridharma perguruan tinggi yang memberikan dampak kepada peningkatan kualitas masyarakat yang dilayani. Universitas Kristen Maranatha adalah salah satu perguruan tinggi berupaya untuk dapat memberikan seluas-luasnya bagi peningkatan kualitas masyarakat dalam kegiatan pengabdian kepada masyarakatnya. Kami para dosen KBK Kewirausahaan dan KBK Pemasaran sebagai salah satu bagian dari Universitas Kristen Maranatha mewujudkan hal tersebut melalui kegiatan pengabdian kepada masyarakat di GKP Tamiyang Indramayu. Adapun kegiatan pengabdian masyarakatnya membahas tentang konsep pemasaran dan implikasinya terhadap pemasaran produk khas Tamiyang. Metode pelaksanaan kegiatan PKM dilakukan dengan pelatihan, berupa pemaparan mengenai konsep pemasaran dan beberapa hal yang dapat diaplikasikan dalam pemasaran produk khas Tamiyang. Dengan pelatihan konsep pemasaran ini diharapkan dapat menemukan potensi pasar dan meningkatkan pengetahuan konsumen potensial terhadap produk khas Tamiyang, sehingga dapat menjadi suatu strategi dalam optimalisasi pemasaran produk khas Tamiyang.

FEATURES OF APPLICATION OF THE NATIONAL ORNAMENT IN MODERN FURNITURE DESIGN: AFRICAN TREND

Politics and marketing and socio-cultural aspects manipulate the evolution of design. The objective world of a person, created by designers, leads to changes in human perception of reality, reflecting social changes. The development of modern design, which is within the rigid framework of globalization, is looking for ways to regenerate the humanistic world, experimenting with ethnocultural identity. Elements of national and traditional art, in particular, ornament, become one of the instruments of the designer, who forms a new aesthetic. Using national and ethnic traditions with the help of images, ornaments, color palettes, and materials, the goal of modern design is to find new ways to meet the new consumer paradigm - creating a unique product that reflects local, personal, and emotional components, thus avoiding the globalization processes

Consumers’ choices between products with different uniqueness duration

Purpose This study aims to introduce the duration of uniqueness, an important dimension of unique products. It studies how choices between products with long versus short duration of uniqueness are influenced by the interaction between pressure and consumers’ need for uniqueness (NFU). Design/methodology/approach This research uses a multi-method study approach. A pilot field-study tested the novelty and importance of the research by asking retail professionals to predict the choice of a hypothetical consumer. A retrospective study assessed the importance of duration of uniqueness in unique product choices, by asking consumers about a real and recent unique product purchase. Four additional experimental studies directly tested hypotheses by manipulating pressure and by measuring or manipulating uniqueness motivations. Findings The pilot field-study showed the novelty and relevance of this research for professionals. Study 1 revealed that, retrospectively, uniqueness duration was considered important for the choice of unique products, by high-NFU consumers under pressure. Studies 2 and 3 demonstrated that pressure increases the tendency of high-NFU, but not low-NFU, consumers to choose products with long over short uniqueness duration. Study 4 provided initial evidence for the process behind the effect. Study 5 showed that considerations of uniqueness duration when choosing mediated the effects. Research limitations/implications The results of the pilot field-study and retrospective study might be affected by recall bias or lay theories. The findings need to be replicated with other sources of pressure and uniqueness. This calls for further research. Practical implications Results are important for companies marketing unique products and they suggest that pressure-based marketing appeals can be used strategically to increase sales of products with long uniqueness duration but decrease sales of products with short uniqueness duration. Although the research provides these guidelines, managers should consider the ethical implications of pressure strategies. Originality/value This is the first attempt to empirically investigate the duration of uniqueness. Although extant research has examined choices between products with different degrees of uniqueness, this research studies choice of products with similar degrees of uniqueness, but different uniqueness duration. Thus, this research adds to the scarce literature studying the duration of symbolic benefits. Moreover, although pressure and NFU frequently co-exist in uniqueness consumption settings, this study is the first to study their joint effects.

On the order of the non-primes of type 6n+5 and 6n+1

The fundamental importance of prime numbers for mathematics is that all other natural numbers can be represented as a unique product of prime numbers[1]. For centuries, mathematicians have been trying to find an order in the occurrence of prime numbers. Since Riemann´s paper on the number of primes under a given size, the distribution of the primes is assumed to be random[2]. Here, I show that prime numbers are not randomly distributed. Their positions are determined by the order of occurrence of the nonprimes of types 6n+5 and 6n+1. By using parametric sine functions, I will show here that all assumptions known today regarding the distribution of prime numbers larger than 3 are wrong. In particular, this refutes Riemann´s hypothesis of random distribution of prime numbers. Furthermore, I will show an exact primality test based on these parametric sine functions, which only uses one parameter.

On the order of the non-primes of type 6n+5 and 6n+1

The fundamental importance of prime numbers for mathematics is that all other natural numbers can be represented as a unique product of prime numbers[1]. For centuries, mathematicians have been trying to find an order in the occurrence of prime numbers. Since Riemann´s paper on the number of primes under a given size, the distribution of the primes is assumed to be random[2]. Here, I show that prime numbers are not randomly distributed. Their positions are determined by the order of occurrence of the nonprimes of types 6n+5 and 6n+1. By using parametric sine functions, I will show here that all assumptions known today regarding the distribution of prime numbers larger than 3 are wrong. In particular, this refutes Riemann´s hypothesis of random distribution of prime numbers. Furthermore, I will show an exact primality test based on these parametric sine functions, which only needs the calculation modes +, -, · , : and only uses one parameter. There is no such deterministic primality test existing until today[3] [4].

Unique product groups and congruence subgroups

We prove that a uniform pro-[Formula: see text] group with no non-abelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche–Wendt groups.