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I-510 (cancelled) Arizona
Proposed in the late 1950s, I-510 would have been a short spur in Phoenix, running north from I-10 along 7th St. to end at Van Buren St. AASHO approved this numbering on Nov. 10, 1958. 
At some point, the planned I-510 was moved eastward to 20th St. In the early 1960s, a 1/2-mile stub of I-510 was built here from I-10 to Buckeye Road. For a short while, this was signed I-510, then was changed to "Buckeye Road/Airport". Richard C. Moeur has seen a photo of an I-510 guide sign, but has not (since 1968) seen it marked that way in real life.  The January 1966 issue of Better Roads has a similar picture. Mike Ballard also spotted it on a 1968 map. 
510 becomes part of 410 (I think)
Some time in the 1960s, I-510 became part of a planned rectangular loop around downtown Phoenix. The bottom and left sides (today, the southernmost miles of I-17) would have been I-10, while the top and right sides would have become I-410. At the time I-410 was added (1968) , I-510 was probably deleted, if not earlier.
3.04 miles ; south from I-10 east of New Orleans. The highway continues south as Paris Road (LA 47). It was completed some time in the mid-1990s. It's part of the canceled southern beltway (I-410), which would have connected with I-310 to the west.
510 - 310 connection to be revived?
Lousiana plans to extend I-510, and there are two plans circulating. The smaller concept: connecting to the West Bank Expressway (US 90 Business).  The larger: a 43-mile 4-lane freeway connecting I-310 and existing I-510. The project includes a Chalmette Bridge, and the rough estimate is $1 billion. 
Oddly enough, this would revive the old I-410 proposal.