Peter says the prophets searched and inquired carefully about the grace that was to come, serving not themselves but later hearers (1 Peter 1:10–12). He adds that these are things “angels long to look” into (1 Peter 1:12).
In 1 Peter 1:10–12, the writer says the deliverance his readers are experiencing was not an afterthought. This section sits inside the opening encouragement that celebrates a “living hope” and an inheritance, while also preparing readers for present hardship (1:3–9).
Peter treats “this salvation” as the long-awaited goal of Israel’s prophetic message. The prophets did not merely predict; they intensely tried to understand what they were announcing (verse 10). Their focus was “the grace that would come to you,” meaning Peter’s present audience are the main beneficiaries of what earlier prophets spoke.
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with 1 Peter 1:10-12, then read the surrounding section so the answer stays connected to the passage's flow.
10Concerning this salvation, the prophets sought and searched diligently, who prophesied of the grace that would come to you,
11searching for what or what kind of time the Spirit of Christ, which was in them, pointed to, when he testified beforehand the sufferings of Christ, and the glories that should follow them.
12To whom it was revealed, that not to themselves, but to you, did they minister these things, which now have been announced to you through those who preached the gospel to you by the Holy Spirit sent forth from heaven; which things angels desire to look into.