- 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 .

Papadimitriou'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 - --- 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 .

>

> Papadimitriou'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

I added some comments to the following address :

http://www.primepuzzles.net/conjectures/conj_049.htm

Best regards,

Patrick Capelle