Re: Two elementary conjectures

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Message 1 of 2 , Oct 15, 2006
--- In primenumbers@yahoogroups.com, Patrick Capelle wrote :

> Dear List,
> A few days ago i proposed two conjectures.
>
> Conjecture A :
> Every natural number n > 1 can be written as n = pq + rs,
> where p, q, r, s are primes or 1.
>
> Conjecture B :
> Every natural number n > 33 is the sum of two semiprimes.
>
> Carlos Rivera checked them up to 10^6.
>
> The conjecture A and the conjecture B were inspired respectively by
> the Papadimitriou's conjecture and the Firoozbakht's conjecture .
>
> Every prime number p > 3 can be written as p = 2q + 3r,
> where q, r are primes or 1.
>
> Firoozbakht's conjecture :
> Every prime number p >= 19 can be written as p = 2q + 3r,
> where q, r are odd primes.
>
> About the conjecture B, Farideh Firoozbakht mentioned recently that
> Lior Manor had already written on this topic (Aug 13 2002) :
> http://www.research.att.com/~njas/sequences/A072966
>
> Do you know other former references ?
>
> Patrick Capelle

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