When G. Moore made his prediction, the number of transistors in a single chip was roughly 32 and today there are approximately half a billion transistors integrated on a single microprocessor.
The April 19, 1965 Electronics magazine was the 35th anniversary issue of the publication. Located obscurely between an article on the future of consumer electronics by an executive at Motorola, and one on advances in space technologies by a NASA official is a less than four page (with graphics) article entitled, "Cramming more components onto integrated circuits," by Gordon E. Moore, Director, Research and Development Laboratories, Fairchild Semiconductor. Moore had been asked by Electronics to predict what was going to happen in the semiconductor components industry over the next 10 years -- to 1975. He speculated that by 1975 it was possible to squeeze as many as 65,000 components on a single silicon chip occupying an area of only about one-fourth a square inch. His reasoning was a log-linear relationship between device complexity (higher circuit density at reduced cost) and time: "The complexity for minimum component costs has increased at a rate of roughly a factor of two per year. Certainly over the short term this rate can be expected to continue, if not to increase. Over the longer term, the rate of increase is a bit more uncertain, although there is no reason to believe it will remain nearly constant for at least 10 years." (Moore 1965)
This was an empirical assertion, although surprisingly it was based on only three data points.
Officially, Moore's Law states that circuit density or capacity of semiconductors doubles every eighteen months or quadruples every three years. It even appears in mathematical form:
(Circuits per chip) = 2(year-1975)/1.5
In 1995 Moore compared the actual performance of two device categories (DRAMs and microprocessors) against his revised projection of 1975. Amazingly, both device types tracked the slope of the exponential curve fairly closely, with DRAMs consistently achieving higher densities than microprocessors over the 25 year period since the early-1970s. Die sizes had continued to increase while line widths had continued to decrease at exponential rates consistent with his 1975 analysis.
The scaling of MOSFETs, Moore’s law, and ITRS. http://userweb.eng.gla.ac.uk/fikru.adamu-lema/Chapter_02.pdf 19.10.2015.