Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , ...Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.展开更多
The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The ma...The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.展开更多
Background Molecular testing is more precise compared to serology and has been widely used in genotyping blood group antigens. Single nucleotide polymorphisms （SNPs） of blood group antigens can be determined by the ...Background Molecular testing is more precise compared to serology and has been widely used in genotyping blood group antigens. Single nucleotide polymorphisms （SNPs） of blood group antigens can be determined by the polymerase chain reaction with sequence specific priming （PCR-SSP） assay. Commercial high-throughput platforms can be expensive and are not approved in China. The genotype frequencies of Kidd, Kell, Duffy, Scianna, and RhCE blood group antigens in Jiangsu province were unknown. The aim of this study is sought to detect the genotype frequencies of Kidd, Kell, Duffy, Scianna, and RhCE antigens in Jiangsu Chinese Hart using molecular methods with laboratory developed tests. Methods DNA was extracted from EDTA-anticoagulated blood samples of 146 voluntary blood donors collected randomly within one month. Standard serologic assay for red blood cell antigens were also performed except the Scianna blood group antigens. PCR-SSP was designed to work under one PCR program to identify the following SNPs： JK1/JK2, KEL 1/KEL2, FYA/FYB, SC1/SC2, C/c and E/e. Results Serologic antigen results were identical to the phenotypes that were predicted from genotyping results. The allele frequencies for Jk^＊01 and Jk^＊02 were 0.51 and 0.49, respectively; for Fy^＊A and Fy^＊B 0.94 and 0.06; for RHCE^＊C and RHCE^＊c 0.68 and 0.32; and for RHCE^＊E and RHCE^＊e 0.28 and 0.72. Among 146 blood donors, all were KEL^＊02/ KEL^＊02 and SC^＊01/SC^＊01, indicating allele frequencies for KEL^＊02 and SC^＊01 close to 1.00. Conclusions The use of PCR-SSP working under the same condition for testing multiple antigens at the same time is practical. This approach can be effective and cost-efficient for small-scale laboratories and in developing counties. These molecular tests can be also used for identifying rare blood types.展开更多
文摘Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.
文摘The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.
文摘Background Molecular testing is more precise compared to serology and has been widely used in genotyping blood group antigens. Single nucleotide polymorphisms （SNPs） of blood group antigens can be determined by the polymerase chain reaction with sequence specific priming （PCR-SSP） assay. Commercial high-throughput platforms can be expensive and are not approved in China. The genotype frequencies of Kidd, Kell, Duffy, Scianna, and RhCE blood group antigens in Jiangsu province were unknown. The aim of this study is sought to detect the genotype frequencies of Kidd, Kell, Duffy, Scianna, and RhCE antigens in Jiangsu Chinese Hart using molecular methods with laboratory developed tests. Methods DNA was extracted from EDTA-anticoagulated blood samples of 146 voluntary blood donors collected randomly within one month. Standard serologic assay for red blood cell antigens were also performed except the Scianna blood group antigens. PCR-SSP was designed to work under one PCR program to identify the following SNPs： JK1/JK2, KEL 1/KEL2, FYA/FYB, SC1/SC2, C/c and E/e. Results Serologic antigen results were identical to the phenotypes that were predicted from genotyping results. The allele frequencies for Jk^＊01 and Jk^＊02 were 0.51 and 0.49, respectively; for Fy^＊A and Fy^＊B 0.94 and 0.06; for RHCE^＊C and RHCE^＊c 0.68 and 0.32; and for RHCE^＊E and RHCE^＊e 0.28 and 0.72. Among 146 blood donors, all were KEL^＊02/ KEL^＊02 and SC^＊01/SC^＊01, indicating allele frequencies for KEL^＊02 and SC^＊01 close to 1.00. Conclusions The use of PCR-SSP working under the same condition for testing multiple antigens at the same time is practical. This approach can be effective and cost-efficient for small-scale laboratories and in developing counties. These molecular tests can be also used for identifying rare blood types.
