## Two elementary conjectures

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• 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
Message 1 of 2 , Oct 8, 2006
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
http://www.research.att.com/~njas/sequences/A072966

Do you know other former references ?

Patrick Capelle
Message 2 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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