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There are infinitely many primes of form a^2+1

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  • 逢绥 刘
    I have posted a paper ¡°There are infinitely many primes of form a^2+1¡±£º http://www.paper.edu.cn/privatetools/released/download.jsp? file=200611-738
    Message 1 of 1 , Nov 28, 2006
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      I have posted a paper “There are infinitely many primes of form a^2+1”:
      http://www.paper.edu.cn/privatetools/released/download.jsp? file=200611-738
      Welcome share, comment, argue or point out a deadly error.

      In this paper we founded a formal system of second order
      arithmetic < P(N), +, \times, 0, 1, \in > by extending the
      operations +, \times on natural numbers to the operations
      on finite sets of natural numbers. We design a new algorithm
      on the congruence classes to obtain a recursive formula
      of the set sequence T'_{i} which approaches the set of all
      numbers a making a^{2}+1 primes. Considering that the number
      of elements |T'_{i}| of the set sequence T'_{i} is strictly
      increasing and the cardinal function |T'_{i}| is continuous with
      respect to the order topology of T'_{i} , we proved that there
      are infinite many primes of the form a^{2}+1. Finally, we extend
      this result to attack the problem of prime infinity in general

      An admissible polynomial with integral coefficients and positive
      leading coefficients, if it represents 2 primes, then it will represent infinitely
      many primes.

      In paper I give a formal solution of “The Ross-Littwood paradox”.

      Liu Fengsui.


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