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Three elementary conjectures about the prime numbers.

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  • Patrick Capelle
    They are presented at the same time because they have formal similarities. Conjecture A : Pi((m+1)^n) - Pi(m^n) = m^(n-2) for n = 2, m = 1. Conjecture B :
    Message 1 of 1 , Sep 9, 2005
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      They are presented at the same time because they have formal
      similarities.

      Conjecture A :
      Pi((m+1)^n) - Pi(m^n) >= m^(n-2)
      for n >= 2, m >= 1.

      Conjecture B :
      Pi((p_(m+1))^n) - Pi((p_m)^n) >= m^(n-1)
      for n >= 1, m >= 1.

      Conjecture C :
      Pi((p_(m+1))^n) - Pi((p_m)^n) >= (p_(m+1))* m^(n-2)
      for n > 2, m >= 1.


      Regards,
      Patrick Capelle.
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