Generalization of Goldbach's conjecture
Using three primes and basic mathematical operations as building blocks, these are the possible combinations to try to create all integers:
combination: all numbers?
p+p+p yes (Goldbach)
(p+p)-p yes
(p-p)-p yes
(p-p)+p yes
(p*p)+p yes
(p*p)-p yes
(p+p)*p not
(p-p)*p not
(p/p)*p not
p*p*p not
(p/p)+p not
(p/p)-p not
(p/p)/p not
The conjecture is that
if (from left to right) the first mathematical operation is division
if the second mathematical operation is multiplication
then: it is impossible to build every number using only primes
(of course, this is obvious: the result of the division of a prime with another prime is not an integer; and the multiplication with a prime number results that certain numbers (odd numbers) became unreachable)
BUT: if these exclusionary reasons do not exist (if the logic of the mathematical operation does not exclude), it is possible to consctruct every integer using only three primes.
Zoltan Galantai
May 19. 2018