Greetings and thank you for your interest in Primary Arms Products. This optic has a 1 inch diameter however this scope mount is intended for 30 millimetre optics. This will not work for the Nikon optic.
Greetings and thank you for your interest in Primary Arms product. The Nikon ProStaff Rimfire 4-12x40 has a 1 in tube diameter and the Primary Arms scope mount you are inquiring about has 30 mm rings. They would not be a good match. I recommend an scope mount designed for 1" inch tubes.
Greetings and thank you for your interest in Primary Arms Optics products. I've taken a look into this for you and the Nikon ProStaff has a tube diameter of 1 inch while the Primary Arms basic scope mount is set for 30 millimetre tube diameter. The 1 inch diameter is slightly smaller than 30 millimetre, so it would cause your smaller tube to shift while mounted due to the extra space. I recommend a scope mount or rings that are made for 1 inch tubes.