The Goldbach conjecture (see Abstract and Definitions) states that every even integer e [greater than or equal to] 4 is goldbach.
1) The Goldbach conjecture holds if and only if for every integer n [greater than or equal to] 1, we have [g.
n+1], then the Mersenne primes conjecture is a special case of the Goldbach conjecture.
4) is easy (indeed, suppose that the Goldbach conjecture holds, then (by using property (2.
n,1] > n, then the Mersenne primes conjecture is an obvious special case of the Goldbach conjecture and there are infinitely many Mersenne primes.
2] 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.
3] 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.
4] 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.
1] Ikorong Anouk Gilbert Nemron, An original symposium over the Goldbach conjecture, The Fermat primes, The Fermat composite numbers conjecture, and the Mersenne primes conjecture, Mathematicae Notae.
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.
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.
A prize of $1 million recently offered by a British publisher, promoting a novel in which a mathematician seeks to prove the Goldbach conjecture, could well stimulate the additional research needed to crack the problem.