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Which aircraft was the MiG-25 designed against?
Short answer
Not a single aircraft: the MiG-25 was designed to intercept high-altitude, high-speed aircraft such as the F-108 Rapier program, the Mach-3-capable XB-70 Valkyrie, and, more importantly, the A-12 from which the SR-71 emerged. Mikoyan's OKB has stated that the main motive was countering the A-12/YF-12 program.

A Mach 3 requirement
In early 1958, a requirement was issued for manned interceptors capable of reaching 3,000 km/h (1,600 kn) and altitudes of up to 27 km (89,000 ft). Work on the new Soviet interceptor that would become the MiG-25 began in mid-1959, a year before Soviet intelligence learned of the American A-12 reconnaissance aircraft, also capable of Mach 3.
Several threats, not just one
The MiG-25 was designed to intercept high-altitude, high-speed aircraft such as the F-108 Rapier program, the Mach-3-capable XB-70 Valkyrie, and, more importantly, the A-12, from which the SR-71 spy plane emerged. Some argue that the threat posed by the XB-70 was the main and sole reason for the design, but the MiG OKB has revealed that the main motive was to counter the A-12/YF-12 program. North American's B-70 Valkyrie, capable of Mach 3, was under development at the time. It is not clear whether the design was influenced by the American XF-108 Rapier and the A-5 Vigilante.
The program went ahead anyway
When development of the XB-70 Valkyrie was halted, that of the MiG-25 continued. As an interceptor, its typical armament includes four long-range R-40 air-to-air missiles.
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