Do you already know about this? I heard about it last night, as I started a series at a church on the formation of the Bible. Afterward someone asked me whether Shakespeare was involved in translating the KJV, since in Psalm 46 the word 'shake' is the 46th word and the word 'spear' is the 46th word from the end, and Shakespeare would have been 46 around the time of the publication of the translation. Well, I had never heard this before, so I said I'd check into it.
Didn't take a lot of searching to discover all of the following.
There are some people who are not completely nuts who think this Shakespeare bit is possible. For example, William Harmon (English prof., UNC) wrote an article a couple decades ago in which he considered it possible. Also, an English prof. at Taylor University, Dennis Hensley, considers it likely.
On the other hand, Hannibal Hamlin, English prof. at Ohio State and expert on things relevant to this subject, thinks it absurd. Personally, I'm going with this opinion, but not for all the reasons Hamlin gives. He criticizes the idea partly because Shakespeare was no Greek and Hebrew scholar. But the idea, as promoted by someone like Harmon, is not that Shakespeare actually translated the psalm, but that he took a translation produced by linguists and polished up the poetry. I think the idea is farfetched just because there's absolutely no evidence for it (Shakespeare's name doesn't appear anywhere in connection with the translation, for instance), only this neat little number game in one psalm.
I'm not sure where the idea came from. Hamlin says it goes back to the 1890s, but he doesn't cite anything (at least not in that online article). Something similar to this idea can be found in one of Rudyard Kipling's stories, Proofs of Holy Writ, published in Strand magazine in 1934. In that story, Shakespeare and Ben Johnson work on enhancing the literary quality of Isaiah 60.
Our exact idea appears in two published works by Anthony Burgess (author of A Clockwork Orange): his biography of Shakespeare published by Knopf in 1970 (pp. 233–34) and his Enderby's Dark Lady (1984), pp. 24–34. In both places, Burgess just suggests the idea as possible. This response to Harmon's article (linked above) by Paul J. C. M. Franssen is very helpful for unraveling some of these details. (BTW, Harmon says he did not get the idea from Burgess, but neither did he think it up himself.)