The invention claimed in an expired, invalid, or otherwise unenforceable patent may be in the public domain. I don't really know what you mean by:
A lot of HYIP are claiming it's "(under public domain)", and they may claim usage of the word "public domain" as being published on Google.
But figuring out whether or not the claims of an issued patent are currently enforceable can be tricky. For example, just figuring out the expiration date of a patent, barring any other intervening circumstances, is a several stage process:
First, what is the basic term of the patent?
In the mid-90s, there was a change in the law about how to calculate terms going forward, so you need to figure out what side of the line the patent is on. Patents that issued from applications filed on or after June 8, 1995, have a term that begins on the date the patent issued and ends twenty years from the date on which the application was filed. This is called the "twenty-year term."
Patents issued before June 8, 1995, or issuing from applications filed before June 8, 1995, have a term that is the greater of (1) the twenty-year term or seventeen years from
the date the patent issues.
So an application that was filed on June 8, 1995 and issued as a patent on April 5, 1997, would have a term that ran from April 5, 1997, to June 8, 2015.
But the application underlying the '010 patent was filed on June 5, 1995, (and issued June 10, 2003) so the second analysis applies and its term is the greater of:
(a) twenty years from the date on which the application was filed - June 5, 2015
(b) 17 years from the date on the patent issues - June 10, 2020
So the basic term of the '010 patent would be from June 10, 2003 to June 10, 2020.
Second, does the patent claim priority to an earlier filed application?
If it does, figuring out the effect can be a complex process and, since the '010 patent does not claim priority to any earlier applications I'm not going to go into detail here - but the one point I'll make is that just because a patent claims priority to an earlier filed application on its face, it doesn't necessarily mean the patent is actually entitled to do so - you should make sure the patent complies with all the statutory requirements.
Third, did the applicant have to make a "terminal disclaimer"?
An applicant can avoid a "non-statutory double patenting" rejection of an application by making a "terminal disclaimer" (an explanation of that kind of rejection would be too much here, but it comes up pretty frequently. See MPEP 804).
A terminal disclaimer is a statement by the applicant in the prosecution file history that he/she "disclaims" part of their patent term. It can either state the patent term ends on a particular date or, more commonly, ends on whatever date some other, earlier patent's term ends. The pre/post June 8, 1995 term calculation can make this a bit complicated, but since the '010 patent does not seem to have a terminal disclaimer associated with it, we don't need to worry about that. (See MPEP 2701 if you're interested.)
Fourth, finally, was the applicant entitled to a patent term extension?
Under certain circumstances, if the PTO takes too long to examine a patent application, the applicant will be entitled to have the term of the patent extended to make up for the delay. This rule does not apply to pre-June 8, 1995 applications, so we don't have to worry about it here. However, it's worth noting that the PTO has gotten into trouble more than once for miscalculating extensions. As with claims to priority, use the information on the face of a patent as a starting point, but before you take any actions in reliance on that information, you should always dig into the details and figure it out yourself.
So, after all that, 010 patent could be in force until June 10, 2020. However, two other factors may also come into play.
First, the patent could have been invalidated or found to be unenforceable during litigation (or during a reexamination proceeding at the PTO). Statistically, this only applies to a tiny fraction of patents, but if you need to rely on whether or not the patent is in force, it's worth checking. (I didn't check for the '010.)
Second, the patent could have expired early.
35 USC 41 requires a patentee to pay periodic "maintenance fees" to keep their patent in force
- 3 years and 6 months after grant, $900
- 7 years and 6 months after grant, $2,300
- 11 years and 6 months after grant, $3,800
You can find out whether or not a patentee has been keeping up on maintenance fees by looking up the patent on the Patent Application Information Retrieval (PAIR) site. (You can actually find out a ton of useful information here.)
Looking up the '010 patent on PAIR, it turns out it expired for failure to pay maintenance fees in 2007. Under some circumstances the patentee can claw this back, but it's probably unlikely in this case.
So yes, I'd say the claims of the '010 patent are in the public domain.
(and I'd normally just check PAIR first, but I thought I'd trick you into reading a long winded explanation.)