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.