Goldbach conjecture

Every even integer greater than 2 can be expressed as the sum of two primes.

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New theories reveal the nature of numbers

http://benvitale-funwithnum3ers.blogspot.com/2011/01/new-theories-reveal-nature-of-numbers.html

Online tool to test Goldbach's conjecture on submitted integers.

http://wims.unice.fr/wims/wims.cgi?module=tool/number/goldbach.en

For example,

0 ..................... 10 .......................... 20

10 = 3 + 7 ... ...10 = 5 + 5

20 = 3 + 17 .... 20 = 7 + 13

0 ....................... 50 ......................... 100

50 = 3 + 47 ... 50 = 7 + 43 ... 50 = 13 + 37 ... 50 = 19 + 31

100 = 3 + 97 ... 100 = 11 + 89 ... 100 = 17 + 83 ... 100 = 29 + 71 ... 100 = 41 + 59 ...
100 = 47 + 53

0 ........................ n .......................... 2n

Goldbach conjecture verification

Let n be an even number larger than two, and let n=p+q, with p and q prime numbers, p<=q,

be a Goldbach partition of n. Let r(n) be the number of Goldbach partitions of n. The number of ways of writing n as a sum of two prime numbers, when the order of the two primes is important, is thus R(n)=2r(n) when n/2 is not a prime and is R(n)=2r(n)-1 when n/2 is a prime. The Goldbach conjecture states that r(n)>0, or, equivalently, that R(n)>0, for every even n larger than two.

http://www.ieeta.pt/~tos/goldbach.html

A lesser known Goldbach Conjecture

http://benvitale-funwithnum3ers.blogspot.com/2011/02/stern-primes.html

What is known :

(1) Schnirelmann(1930): There is some N such that every number from some point onwards

can be written as the sum of at most N primes.

(2) Vinogradov(1937): Every odd number from some point onwards can be written as

the sum of 3 primes.

(3) Chen(1966): Every sufficiently large even integer is the sum of a prime and

an "almost prime" (a number with at most 2 prime factors).