Is a patent holder required to disclose their patent # on their website and products?

They must mark the product with the patent number. An apparatus must bear the patent number on itself of in some cases just the packaging. Methods of course have no place to put a patent number so that is shown in the advertising material etc. For a full explanation of this google "patent marking".

A patent owner has the duty to mark his invention with his patent number to provide notice to the public. Failure to do so will prevent the patent owner from acquiring damages in an infringement action. If patent owner later marks his invention with the patent number, damages will only accrue starting from the date of the patent marking.

A patent owner is encouraged, but not required, to put the patent number on its products - or the word "patented" - so you are put "on notice" regarding these rights. When the patent owner fails to "mark the product" - they give up the right to claim damages from any infringement - until they give full notice of the patent to the infringer. At that point, the infringer runs the risk of being found to be a "willful infringer" for continued use of the patented invention - which can lead to treble (3X) damages being awarded to the patent owner.

There is no requirement that the patent holder publish their patent number. However, for triple damages to apply, the infringer must have known about he patent, so you lose a lot of potential leverage if you don't publish it.