Sum of prime and semiprime conjecture

Importance: Medium ✭✭
Author(s): Geoffrey Marnell
Subject: Number Theory
Keywords: prime
semiprime
Recomm. for undergrads: no
Posted by: princeps
on: March 23rd, 2012

\begin{conjecture} Every even number greater than $10$ can be represented as the sum of an odd prime number and an odd \Def {semiprime} . \end{conjecture}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}

Bibliography

% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

*[M] Geoffrey R. Marnell, "Ten Prime Conjectures", Journal of Recreational Mathematics 33:3 (2004-2005), pp. 193--196.


* indicates original appearance(s) of problem.

surely that's Chen's theorem

Every sufficiently large even number is the sum of either 2 primes or a prime and a semiprime.

Yes, apart from the

Yes, apart from the "sufficiently large" and allowing prime + prime as well as prime + semiprime. The parity problem makes the latter hard, but some progress has been made, see arXiv:math/0609615 and arXiv:0803.2636. (The key progress is their use of E2 = semiprimes rather than P2 = primes or semiprimes.)

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