I hunted them for years when I lived in the Black Hills. Always used a 25/06 with 117 gr Sierra bullets.
Pronghorns are small. They're easy to put down. I wanted a round that would shoot flat and accurately and not damage much meat. The 25/06 with a 10X Redfield silhouette scope worked just fine.
My closest shot was at 125 yds (running and no, I didn't hit the one I was aiming at, I hit the 3rd one behind him
) and the longest was at 365 yds.