ON THE REPRESENTATION OF A LARGE EVEN INTEGER AS THE SUM OF A PRIME AND THE PRODUCT OF AT MOST TWO PRIMES

I For the sake of brevity, we denote the following proposition by (1,α): Every sufficiently large even integer is the sum of a prime and the product of at most α primes. Selberg’s method and some results in the theory of Dirichlet L-function have been employed by many mathematicians to prove the above proposition, for example, (1,5) (Pan Cheng-tung,); (1,4) (Wang Yuan, Pan Cheng-tung,); (1,3) The aim of the present note is to give a sketch of the proof of (1,2). Details will be published later elsewhere.