As seems to be the case with so many companies, Remington wanted its customers use their components to reload their shells. While Remington enjoyed a substantial portion of the U.S. shotgun shell market, the 209 sized primer used by Winchester, Alcan, CCI, Federal and others became the defacto standard.

Box of 209 sized Remington 97 primers and smaller diameter 57 primers. Note that the primer cups on the No. 97 primers are brass colored while the No. 57 primers are silver colored.
By 1969, the writing was on the wall for the end of the 57. The 209 sized Remington 97 primer had been introduced and was used in the company's new plastic target loads. The smaller 57 primer continued to be used in their game loads for a few years.

Shotshell primer battery cup flash holes; from left to right, Remington 97, Remington 57 and Winchester 209.
It is worth noting that both the Remington 57 and 97 primers have an uncovered flash hole in their battery cups, making them unsuitable for use with modern fine grained powders. These primers are more suitable for use with the old fashioned flake powders such as Red Dot and Unique.