## Conjecture for integer linear combinations of primes

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• Hello All: I send a new conjecture: Conjecture for integer linear combinations of primes ...   Let n a even number , for all 2
Message 1 of 2 , May 5, 2008
Hello All:
I send a new conjecture:
Conjecture for integer linear combinations of primes
:

Let n a even number , for all 2<=k <=n/2 exists one or more integer linear combination:

a1p1+a2p2+..+ampm=n

and

a1+a2++am=k

p1,p2,., pm are all the prime numbers less than n
and ai>=0 integer

Example:

n=10   n/2=5

p1=2, p2=3  p3=5 p4=7

2*5=10                     a1=0, a2=0, a3=2, a4=0      Sai=2
1*3+1*7=10             a1=0, a2=1, a3=0, a4=1      Sai=2
1*2+1*3+1*5=10     a1=1, a2=1, a3=1, a4=0      Sai=3
2*2+2*3=10             a1=2, a2=2, a3=0, a4=0      Sai=4
5*2=10                     a1=5, a2=0, a3=0, a4=0      Sai=5

Q1=Is true or false this Conjecture.
Q2=¿ We can obtain Goldbach Conjecture as a particular case of this conjecture?
Sincerely:
Sebastián Martín Ruiz

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• 1. Conjecture for integer linear combinations of primes Posted by: Sebastian Martin sebi_sebi@yahoo.com sebi_sebi Date: Mon May 5, 2008 4:10 am ((PDT)) Q1=Is
Message 2 of 2 , May 6, 2008
1. Conjecture for integer linear combinations of primes
Posted by: "Sebastian Martin" sebi_sebi@... sebi_sebi
Date: Mon May 5, 2008 4:10 am ((PDT))

Q1=Is true or false this Conjecture.
Q2=¿ We can obtain Goldbach Conjecture as a particular case of this conjecture?
Sincerely:
Sebastián Martín Ruiz

If Goldbach conjecture is true then your conjecture is true
because the

p1 + p2 = n = 2k is the one of one or more linear combination of primes that equal n.

Your conjecture does not imply the Goldbach conjecture, because we can imagine that
the set of linear combinations of primes that equals n, does not include a linear combination of the
form p1 + p2 = n.

Kermit Rose

< kermit@... >
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