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• ## Three elementary conjectures about the prime numbers.

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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 :
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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