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I-84 is the only interstate in 2 sections (I-76, I-86 and I-88 are the other 2-part interstates) to have a 3di on both parts.
Radio station WHAS nicknames itself "Interstate 84," to connote "another highway on the roadmap" of the information superhighway. The 84 comes from its location at 840 AM on your AM dial. Its traffic reports, however, don't cover I-84, because the station serves the good people of... Louisville, Ky.
3.62 miles ; Idaho's only 3-digit interstate; serves Boise.
On Dec. 12, 1968, the Boise West Connector was dedicated; this is now part of today's I-184 leading from I-84.  At the time, I-84 was known as I-80N, and the Connector was I-180N, the only 3-digit interstate that has ever had a letter suffix. (Pennsylvania's I-80S -- now I-76 -- had three 3-digit interstates, but they were known as Interstates 280, 480, and 680, without the suffix.)
The route has also been signed Business Route 84; I don't know which years each designation was in effect. Nick Webster reports that the official 1974 ITD map shows the Connector simply as ID 55. 
On July 1, 1980, at the direction of AASHTO, the letter suffixed I-80N was changed to I-84.   This was part of a larger effort to phase out so-called letter-suffixed interstate numbers; I-15W, also in Idaho, became the western Interstate 86. I-180N followed the I-84 change and became I-184.
In 1990, I-184 was extended to downtown Boise. 
I-184 (cancelled) Rhode Island
If Interstate 84 had been completed to Providence, as was planned in the 1970s, RI 10 between present-day US 6 and I-95 would have been called Interstate 184, according to at least one planning map. 
I-284 (cancelled) Connecticut
I-284 would have run about 5 miles from the I-84/CT 2 interchange north to I-291 in East Hartford.
I-284 died in the mid-80s because of environmental concerns. The Governor Street "Evel Knievel" ramps (I-84 exit 56) were the planned start of the highway.
More details: see I-284 at Connecticut Roads.
8.20 miles ; east from I-84 in East Hartford to US 6 and 44 in Bolton Notch. Interstate 384 was once part of Interstate 84, but became I-384 in 1984 when I-84 was rerouted. It now serves as a Manchester bypass.
More details: see I-384 at Connecticut Roads.
I-484 (cancelled) Connecticut
Never completed, I-484 would have run from I-91 exit 29A west through Hartford, underneath Bushnell park, to connect with I-84 exit 48 near the Capitol.
More details: see I-484 at Connecticut Roads.
I-684 New York; Connecticut
28.47 miles ; from I-84 in Brewster to I-287 in White Plains. Interstate 684 was originally intended to be part of I-87. Its most notable feature is a 1.41-mile cut through a corner of Greenwich, Connecticut, with no interchange in that stretch. No other interstate highway passes through a state while providing no access in that state.
More details: see I-684 at Connecticut Roads.