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A Patriotic Highway
Interstate 76 serves Philadelphia, where the Declaration of Independence was signed in 1776... and the markers are red, white, and blue. Just a coincidence, though; see sidebar ("Meet the Parent").
Also, I-76 was the first highway to have separate eastern and western instances (the western I-76, formerly I-80S, leads from Denver to I-80 in Nebraska). These highways are not connected or related in any way, other than being far enough apart that the 76 number could be reused without confusing anyone.
Furthermore, Marc Fannin notes that Colorado was admitted to the US in 1876, making its I-76 a tip of the hat as well.
Later "split" highways:
It's true: I-86 has existed in three places, but not all at the same time.
Meet the Parent: I-76
The stories of most x76 3di's are intertwined with the birth of, and changes to, Interstate 76. This highway in Pennsylvania comprises the Pennsylvania Turnpike from the Ohio state line to I-276 at King of Prussia, and the Schuylkill Expressway from there to the New Jersey border.
Following are its numbering and route changes over the years.  Note:
The I-76 number is not deliberately chosen to honor Philadelphia's role in the 1776 signing of the Declaration of Independence; it is just a "free" number that happened to fit into the grid.
There is some debate over the eastern and western ends of the new I-76. A BPR regional engineer suggests extending I-76 westward over the entire Turnpike into Ohio, to end at I-71. This is declined in favor of a direct Pittsburgh to Philadelphia route, but is adopted later. Another BRP official suggests routing I-76 over today's I-276 Turnpike segment eastward into New Jersey, but this is declined for similar reasons.Feb. 26, 1964 - I-76 is approved from Pittsburgh to Camden, N. J. along today's I-376, I-76 and I-676. Its 3di's are redesignated I-176, I-276, I-476, and I-676. Jan. 11, 1972 - in response to Ohio's desire to address motorist confusion of I-80 vs. I-80S, and the desire to clean up some routes in Pittsburgh, I-76 is moved from the downtown Pittsburgh terminus to follow the Turnpike into Ohio, ending at I-71. Former I-76 into Pittsburgh becomes I-376. I-279 is also amended, and a short-lived I-876 is renamed I-579. June 19, 1972 - to improve route continuity along the Schuylkill Expressway, AASHO approves a swap of I-76 and I-676 in Philadelphia. The Schuylkill is now I-76; the Vine Street Expressway is I-676.
11.27 miles ; connects Reading to I-76. Originally, "connects" wasn't true, since you had to get off 76 onto surface streets (PA 10) before entering Interstate 176 (this is not unique on the PA Turnpike). In 1996, a new direct connecting interchange opened. I-176 drivers can still access PA 10 using the old connection, which is now Exit 1B. 
The freeway was completed in 1963.  Its original designation was I-180, since I-76 was called I-80s at the time (see "Meet the Parent"). On Feb. 26, 1964, with the creation of I-76, the Reading spur became I-176. 
32.65 miles ; bypasses Philadelphia to the north. Interstate 276 is the easternmost segment (Delaware River Extension) of the Pennsylvania Turnpike, considered by many the nation's first modern expressway.
The main portion of the Pennsylvania Turnpike opened on October 1, 1940. The eastern extension (today's I-276) was completed November 17, 1954.
The I-276 portion of the Turnpike has undergone some numbering changes since the Interstate system was established (see "Meet the Parent"). In the late 1950s, I-80S was considered for this route, but in 1958, the official designation became I-280.  
In 1964, Interstate 80S became Interstate 76, and all its 3-digit auxiliary interstates followed; I-280 became today's I-276. 
Up until 1982, the official length for I-276 was about 33 miles, extending to the Turnpike bridge crossing the Delaware River. The current length (29.88 miles) reflects a planned interchange at I-95. 
Interchange planned at Interstate 95
Currently there is no direct connection between I-276 and I-95, though one has been proposed for decades. In 1969, when I-95 was built, federal funds could not be used to connect an Interstate highway to a toll road. (The laws have since been changed.) A connection has been contemplated since the 1970s. 
Now a $640 million interchange project is planned. Work could start in 2007 and complete by 2012.  Three related projects will also be constructed:
"The 2015-2016 completion date that has been rumored is not the completion date of the interchange, but is the completion date of the last of the three associated projects to be completed. This is the new bridge. The interchange can be built without the widening of the mainline or the addition of a second bridge. It does require the new toll barrier, however." 
14.70 miles ; from I-279 in downtown Pittsburgh to the Pennsylvania Turnpike (I-76) at Monroeville. Part of the Penn-Lincoln Parkway, Interstate 376 is the eastern gateway to the Steel City. Locals call the route "Parkway East"; Parkway West (the Penn-Lincoln Parkway) is I-279 south out of the city. Informally, "Parkway North" is I-279 to points north.  
Or should we call it the Horror Highway? I-376 passes by Monroeville, whose mall was featured in George Romero's "Dawn of the Dead." In Stephen King's novel "Christine," the main character worked a summer on the I-376 construction crew.
By 2009 I-376 will be extended to the west and north, to reconnect with the Pennsylvania Turnpike (I-76) in Beaver County. The dual connection would make an even leading digit more appropriate (such as I-876) -- but more than 30 years of history weighs in favor of keeping the 376 designation.
In the past, however, I-376 has had other numbers, as we shall see.
Planning for a divided highway along today's I-376 dates back to the 1920s. Design work accelerated in earnest during the 1930s and 1940s (see Pennsylvania Highways for detailed history and design diagrams).
The first section, between exits 2B and 10B, opened on June 5, 1953. After more openings from 1956 to 1959, the final section, from Churchill to the Turnpike, opened on Oct. 27, 1962. 
The (nearly) original 1950s Interstate numbering for Parkway East, as of 1958, was I-70. (Today's I-70 south of Pittsburgh was called I-70S, and much of today's I-76 was called I-80S.) 
Over the years, officials in Pennsylvania and Ohio grew dissatisfied with the I-80S designation (see "Meet the Parent") and the number for Parkway East changed two more times. On Feb. 26, 1964, I-76 was created, and Parkway East carried that designation into Pittsburgh. On Jan. 11, 1972, I-76 was redefined to follow the Pennsylvania Turnpike into Ohio; Parkway East gained a spur designation, I-376. 
Westward extension in the works
Around 2000, Allegheny County officials advocated extending I-376 westward and northward along existing freeways to reach I-80 in Mercer County. The reasoning: economic development, and an interstate connection to Pittsburgh's International airport. The revised I-376 would incorporated part of I-279, US 22/30, and PA 60, and would cross I-76 in Beaver County. Several substandard sections of highway would need to be rehabilitated to meet interstate standards if the plan were approved.
In May 2002, Allegheny County Executive James Roddey floated a less ambitious idea: designate "Parkway West" (I-279, US 22/30 and PA 60) as an extension of I-376, leading to Pittsburgh International Airport. It's "the only major airport in the United States that is not served by an interstate or a major U.S. highway," Roddey said. 
In Sept. 2003, officials at a meeting of the Airport Corridor Transportation Association advanced a plan to include parts of Routes 60, 22, 30 and 422 into an extended I-376. PennDOT and FHWA officials met to discuss substandard parts of the proposed route. PennDOT was hoping for permission to put up I-376 signs soon, with the understanding that the route will be upgraded afterward. 
In October 2005, Sen. Rick Santorum (!) and Rep. Melissa Hart announced that on Jan. 1, 2009, I-376 will extend westward along I-279 and US 22/30, and northward along PA 60 to I-76 in Beaver County. This will add 43.5 miles to its length, totaling about 60 miles. About $91 million in improvements would need to take place. 
If 26.4 miles of PA 60 continuing to I-80 were to be added (which is still contemplated), the total length of I-376 would be about 86 miles. 
129.61 miles ; Interstate 476 is the nation's longest 3-digit interstate, running from I-95 southwest of Philly to I-81 northwest of Scranton. The Scranton area has a varied mix of interstates: I-81, I-84, I-380, and I-476.
The original definition of I-476 was the $531 million, 21.5-mile "Blue Route" (from the color of its line on planning maps), from I-95 to I-276. This highway opened on Dec. 19, 1991 after decades on the drawing board.  Though the Philadelphia Inquirer called the highway "the most costly, most bitterly opposed highway in Pennsylvania history," I-476 has some (unspecified) environmentally-friendly features built into its design. . Until the year 2027, I-476 will have spent more years as a dotted line than as pavement.
Blue Route History
In 1951, the Delaware County planning commission asked the Pennsylvania Department of Highways to survey a new north-south route for a "Mid-County Expressway," eliminating a bottleneck on PA 320.
In 1955, the highway was proposed as a branch of the Pennsylvania Turnpike; soon after Interstate legislation, the 90% federal contribution from interstates must have put a sparkle in someone's eye.
In July 1956, the state looked over five different-colored routes on a drawing, eventually choosing the blue one, following the Crum Creek Valley through Nether Providence and Swarthmore. In 1963 the state approved the plan. Construction began in 1967 but was snagged from 1974 to about 1985 by environmental lawsuits and other issues. 
The Blue Route was included in Pennsylvania's interstate highway system, but was originally numbered I-495.  On Nov. 12, 1958, its designation was changed to I-480, as it connected with former Interstate 80S.  In 1964, when I-80S became I-76, I-480 became I-476. Fortunately, no part of I-495/480/476 was yet open, so motorist confusion was minimized.
I-476 extended; vaults to #1
In the 1990s, Pennsylvania (or the Turnpike Authority) advocated extending the I-476 designation along the entire Turnpike Northeast Extension (PA 9) to I-81 north of Scranton. The intent: to help publicize the route for travelers.
On Nov. 11, 1994, AASHTO denied this proposal, citing concerns about the number, substandard design conditions along the route, and the fact that the FHWA had not yet approved the extension. 
On April 22, 1995, however, AASHTO approved the extension.  In a manner of speaking, the western Philly bypass now also bypasses Allentown and Scranton. The renumbering took place November 1, 1996. (Originally, the Northeast Extension was to extend to the New York state line; the abrupt "end of the line" interchange at Scranton shows signs of planned extension.  )
The Blue Route is already very congested in the Philadelphia area; in 1995 Delaware county was fighting with the FHWA on a plan to widen 476 to six lanes south of PA 3.
I-576 (proposed) Pennsylvania
The is a proposed designation for the Southern Beltway, a planned toll road south of Pittsburgh. The 30-mile highway would run from the future Mon-Fayette Expressway, to I-79 near Canonsburg, to the Southern Expressway (PA 60) at Pittsburgh International Airport.
The highway is only in the design stage as of mid-2002. If it is built, it would be designated state route 576 or Turnpike route 576. The Turnpike Commission expects that interstate designation would be approved for the highway in the future.
I-676 Pennsylvania; New Jersey
6.90 miles ; Interstate 676 goes from I-76 through downtown Philadelphia (Vine St. Expressway), across the Ben Franklin Bridge over the Delaware River into Camden, ending at I-76 near the Walt Whitman Bridge. The Camden section was completed around 1980; the Vine Street section (four and six lanes) was completed on Jan. 10, 1991. 
The Ben Franklin Bridge, opened in 1926, carries seven lanes and the PATCO commuter rail line.
The Vine Street Expressway, part of Pennsylvania's interstate system since the 1950s, has undergone some numbering changes since then. (see "Meet the Parent".) The original number was Interstate 895, connecting I-95 to the contemporary I-280. On Nov. 12, 1958, it became part of a rerouted Interstate 80S. 
In 1964, I-80S became I-76, including the Vine Street portion. The remainder of the Schuylkill leading to I-95 was called I-676. In 1972, I-676 was moved to the Vine Street portion, leaving I-76 as a continuous roadway from the Pennsylvania Turnpike to I-95.
Is you is or is you ain't my baby...
Chris Blaney makes a compelling argument that I-676 is actually two distinct interstates, connected by the US 30 highway over the Ben Franklin Bridge: 
"The BFB is *not* Interstate standard *at all*. It's seven lanes, undivided: there aren't even cones separating the two directions of traffic as there are on other undivided bridges.Jeff Taylor, upon reading this, contacted the BRPA, the local agency in charge of the bridges. According to them, the Ben Franklin Bridge is I-676 all the way, so the designation is continuous between the two states. 
I-876 (numbered as another interstate) Pennsylvania