You said: “It appears that the first few numbers relate to a County Code and a Year”
I concur completely on year. Both certificates start with #151, which is consistent with 15=state code for Hawaii used by Census (these are assigned in alphabetical order).
However, currently under the Census FIPS code system, 1=county code for Hawaii, 3=Honolulu. http://www.epa.gov/enviro/html/codes/hi.html
Since both were born in Honolulu County, I would have expected to see 153, not 151. That said, I don’t know when FIPS numbering system began. It could be that in 1961, 1 denoted Honolulu rather than Hawaii County.
I assumed that the string of numbers following birth year simply was the recorded birth order in that year. That’s consistent with Jeremy Smith having a low number 151 1983 000976 for his January birth.
But 151 1930 010259 seems too high for Patricia DeCosta’s May 14 birth. In 2006, Honolulu only had 14,000 births,
http://hawaii.gov/health/statistics/vital-statistics/vr_06/birth.pdf
so somehow I don’t picture this number being >20,000 in 1930. But for those interested in trivia, Don Ho was born in Honolulu the same year as Patricia!
http://en.wikipedia.org/wiki/Don_Ho
It may be that each hospital had a block of numbers assigned to it to be used as required. That would mean that there would be gaps in the numbering sequence. Or, there might be some other piece of information encoded in the six-digit number (male vs. female?) Or maybe they used all the numbers starting with 000001 and when they reached 999999, they started back at 000001 again. The year would certainly be different then, so the numbers would be unique.