But, the Goldbach conjecture
amounts to the claim that there is a non-zero lower bound.
 Ikorong Anouk Gilbert Nemron, An original abstract over the twin primes, the Goldbach Conjecture, the Friendly numbers, the perfect numbers, the Mersenne composite numbers, and the Sophie Germain primes, Journal of Discrete Mathematical Sciences And Cryptography, Taru Plublications, 11(2008), No.
 Ikorong Anouk Gilbert Nemron, A Curious Strong Resemblance Between The Goldbach Conjecture And Fermat Last Assertion, Journal Of Informatics And Mathematical Sciences, 1(2009), No.
 Ikorong Anouk Gilbert Nemron, Runing With The Twin Primes, The Goldbach Conjecture, The Fermat Primes Numbers, The Fermat Composite Numbers, And The Mersenne Primes, Far East Journal Of Mathematical Sciences, 40(2010), 253-266.
(2.1) The Goldbach conjecture holds if and only if for every integer n [greater than or equal to] 1, we have [g.sub.n+1] = 2n + 2.
(2.4) If for every integer n of the form n = 37k (where k is an integer [greater than or equal to] 111), we have 30[m.sub.n,1] [greater than or equal to] [g.sub.n+1], then the Mersenne primes conjecture is a special case of the Goldbach conjecture.
Property (2.0) is immediate (it suffices to use the definition of [g.sub.n+1], via the definition of [g.sub.n]); property (2.1) is obvious (it suffices to use the definition of [g.sub.n+1] (via the definiton of [g.sub.n]) and the meaning of the Goldbach conjecture), and property (2.2) is immediate (indeed, it suffices to use the definition of [m.sub.n,1]).
Recently, in 2000, some new direction of proof of Goldbach conjecture
has been forwarded by Kalita .
(n.d.) Verifying the Goldbach Conjecture up to 4.104.
Goldbach Conjecture. Singapore: World Scientific Publishing Co.
The Goldbach conjecture, devised by historian and mathematician Christian Goldbach in 1742, proposes that every even number is the sum of two primes; for example, 8 = 3 + 5.
"Such computations prove the truth of the Goldbach conjecture for a finite set of even numbers," says Herman te Riele of the National Research Institute for Mathematics and Computer Science in Amsterdam.