Whether or not there’s enough evidence to assert that either Bacon or Shakespeare were Masons, there does seem to be enough to suspect they could have been. And this would help to explain the authorship secrecy with which the Shakespeare works were published since such groups, like Bacon himself, were given to secrecy or privacy. In any case, the number 287 is here related to Francis Bacon.
Besides the link to Masonic history the researchers also believed, rightly or not, that Bacon seemed to be associated with the Rosicrucian activity of the time. And they connected the number 287 to Bacon in this association. They found that in the book Mathematical Magick by Bishop John Wilkins, a founder of the Royal Society, and who was at least associated with several Masons as well as those with Rosicrucian interests [see The Golden Builders, 2002 by Tobias Churton], that on page 136 in the second part of the Wilkins’ book (so there are two page 136s) that after 150 roman words (not counting Italicized words) then the 151st word was the name Francis as part of the symbolic name of Francis Rosicrosse and Wilkins associated this name to the Rosicrucians of the “Confession of that Fraternity”. So the name here being linked to the number 287 (the page number plus the word count), the early Baconian authors experimented and found that a symbolic name of “Fra Rosicrosse” or “Fra Rosiecross” would equal 287 in the Kay count. They had found several instances in letters with Bacon’s first name abbreviated as “Fra”, some signed by him. And as well there was this abbreviation of “Fra” used in one of the testimonials in Bacon’s 1640 Advancement of Learning. They then felt there was justification to hypothesize that this symbolic abbreviated name of “Fra Rosicrosse” represented Francis Bacon. It’s interesting also that both links to the # 287, here and in the First Folio, are found on a page of 136. Also, the word HONORIFICABILITUDINITATIBUS in the First Folio would also be the 151st word in Roman type on the page if the hyphenated word of “almes-basket” were in this case counted as two words. Keep in mind when counting that at one spot the word ‘debt’ is deliberately spelled out as ‘d e b t’ (with spaces) and so each letter is counted as a word as would be ‘a’ or ‘I’ or the first initial of someone’s name. This is because each letter is spoken separately in the play’s scene.
The Wilkins book can be found here:
Wilkins was also quite familiar with ciphers, having coined the word cryptographia, among others, and developed some ciphers himself.
There are other known connections between the Rosicrucian movement and the friends of both Bacon and Shakespeare. Another of Ron Heisler’s many articles in this area is Shakespeare and the Ethos of the Rosicrucians, found here: http://www.levity.com/alchemy/h_shake.html
And as far as the Shakespeare Authorship question is concerned he’s a traditionalist.
Bacon very likely met the Rosicrucian philosopher and inventor Cornelius Drebbel and may have been influenced by him in writing his New Atlantis.