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
For a finite group G, it is denoted by N（G） the set of conjugacy class sizes of G. In 1980s, J. G. Thompson posed the following conjecture： if L is a finite nonabelian simple group, G is a finite group with trivial...For a finite group G, it is denoted by N（G） the set of conjugacy class sizes of G. In 1980s, J. G. Thompson posed the following conjecture： if L is a finite nonabelian simple group, G is a finite group with trivial center, and N（G） = N（L）, then L and G are isomorphic. In this paper, it is proved that Thompson＇s conjecture is true for the alternating group A22 with connected prime graph.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For a finite group G, it is denoted by N（G） the set of conjugacy class sizes of G. In 1980s, J. G. Thompson posed the following conjecture： if L is a finite nonabelian simple group, G is a finite group with trivial center, and N（G） = N（L）, then L and G are isomorphic. In this paper, it is proved that Thompson＇s conjecture is true for the alternating group A22 with connected prime graph.
