Highly suspect to be synthetic if that big, especially if its clean. However, alexandrite value is based on several variables, proof of origin (don't take any vendor's "word for it"), percent of color change, clarity, the saturation and hue of the colorways themselves, among those variables, not just size.
Like TL, I'd be willing to bet your hypothetical stone is a synthetic. Alexandrites of that size were quite rare even back in the heyday of the Ural mines. But to give you some basis for comparison, the gavel price, at a Christie's auction last year, for this 21+ ct loose stone was just shy of $1.5 million, or roughly $70,000/ct: http://www.christies.com/lotfinder/jewelry/an-exceptional-unmounted-alexandrite-5792391-details.aspx
OP: in your year and a half on PS, you have posted 24 times, 13 of which were topics you started. Rather than start so many threads asking fairly basic questions, you may want to devote a little more time and energy to reading up on gemstone types, treatments, prices, etc. where you would find the answers to your questions. To search a topic, there is a "Search by Google" box on the top right of the Colored Stones page where you can search any topic you seek. For example when I searched "Russian alexandrite," it returned 7 pages of threads on the topic.
Depends on the hypothetical colour change strength, hypothetical colouration both ways, hypothetical clarity and hypothetical lab report proving that it is a natural alexandrite.
Not sure what your intention was, but mentioning how many threads someone started etc seems a bit over the top on the "enter euphemism here" side. I didn't know there were restrictions on what people wish to ask about, nor the amount of posts they choose to start.