AS TO THIS SALVATION, THE PROPHETS: peri es soterias ...prophetai: (Ge 49:10; Da 2:44; Hag 2:7; Zec 6:12; Mt 13:17; Lu 10:24; 24:25-27; Lu 24:44; Acts 3:22-24; 7:52; 10:43; 13:27-29; 28:23; 2Pet 1:19 20-21)

Spurgeon...

Salvation (4991) (soteria from soter = savior, deliverer click sozo) and in the OT conveyed the ideas of deliverance from present danger or trouble especially from defeat in battle as well as giving a foretaste by the righteous, after death, of the enjoyment of the age to come. It is into a world such as this that the gospel of salvation came.

Salvation means not just escape from the penalty of sin but includes the ideas of safety, deliverance from slavery, preservation from danger or destruction.

Prophets (4396) (prophetes from pró = before or forth + phemí = tell) were persons in the OT inspired to proclaim or reveal God's will or purpose, through utterance of divinely inspired revelation. A prophet was one who would foretell future events and also one who would exhort, reprove, and even threaten individuals or nations as the ambassador of God and the interpreter of His will to men. The important point to remember is that the prophet spoke not his own thoughts but what he received from God, even though he retained his own consciousness and personality in his forth telling. The prophets were carried along by the Holy Spirit (see note 2 Peter 1:21)

As someone has said “The modern church is a ‘non-prophet’ organization.”

Mills writes that...

The paroemia (short, pithy saying or adage) ‘familiarity breeds contempt,’ holds true for Christianity as well, for I suppose most believers eventually incline to treating their salvation as commonplace. This section’s instruction is intended to counter this tendency by inviting meditation on salvation’s incomprehensible privilege. The section makes tandem arguments to establish the wonder of the grace of salvation-arguing first that the great prophets of the Old Testament were deeply awed by the wonder of the truths about the coming age of grace revealed through them, the grace which all believers experience. The point made is thus simple yet powerful-each believer is in a more privileged position than the Old Testament prophets like Isaiah, Jeremiah, Ezekiel, and Daniel, more privileged than even David and Moses, as our Lord Himself taught (Luke 10:24). The wonder of this position is confirmed, so the epistle argues in the second place, by the fact that angels yearn to examine the glories of this privilege. When these tandem truths are assimilated, there is no room for complacency. This section challenges all believers to meditate on the absolute wonder of being saved, and, besides being an exercise in worshipful thanksgiving, the epistle will use this as the basis for its appeal to sanctified Christian living." (Mills, M.  I Peter : A study guide to the First Epistle by Peter. Dallas: 3E Ministries)

WHO PROPHESIED OF THE GRACE THAT WOULD COME TO YOU: prophetai oi peri tes eis humas charitos propheteusantes (AAPMPN):

Spurgeon...

Observe, dear brethren, that the prophets did not speak without due consideration, but they “enquired and searched diligently” into the meaning of that salvation of which they “testified beforehand.” Holy Scripture must not be read by us carelessly. We ought to peer, and pry, and search into it to get at its hidden meaning, and the prophecies as well as the rest of the Word are to be searched into by us upon whom the ends of the earth have come.

Prophesied (4395) (propheteuo from pró = before or forth + phemí = tell) means in this case to speak under inspiration and foretell things to come or to declare truths through the inspiration of God’s Holy Spirit.

The prophet was a proclaimer who spoke out the counsel of God with clearness, energy, and authority which spring from the consciousness of speaking in God’s name and having received a direct message from Him to deliver.

The "grace that would come" is the prophecy fulfilled by Paul's description that

the grace of God has appeared, bringing salvation to all men (see note Titus 2:11; 2:12; 2:13). (See related resource Messianic Prophecies)

Grace (5485)(charis) is a word with a number of meanings in the NT, the specific nuance being dependent on the context.

(1) a quality that adds delight or pleasure or a winning quality or attractiveness that invites a favorable reaction = graciousness, attractiveness, charm, winsomeness  (Luke 4:22, Colossians 4:6)

The prophesied coming "grace of God" which "has appeared" is no less than the Messiah, Who through His suffering and sacrifice has flung wide open the flood gates of salvation by grace to all who would receive and believe.

MADE CAREFUL SEARCH AND INQUIRY: peri es soterias exezetesan (3PAAI) kai exeraunesan (3PAAI):  (11; Pr 2:4; Da 9:3; Jn 5:39; 7:52; Acts 17:11)

The prophets not only spoke to the situation of their contemporaries, but they also spoke of the longed-for messianic times. In predicting the future, they did not always understand their utterances. The clearest example is Daniel and his visions (Da 8:27; 12:8) and his study of other prophets (Da 9:2). The prophets longed to see the messianic age and so searched into what they could know of it (cf. Lu 10:24) but their divine inspiration did not bestow omniscience.

Careful search (1567) (ekzeteo from ek = intensifies the meaning of zetéo = seek, the preposition "ek" in compound always seems to denote that the seeker finds or at least exhausts his powers of seeking) means to seek out, search diligently for anything lost, to seek in order to obtain or know and to exert considerable effort and care in learning something.

Inquiry (1830) (exereunao from ek = an intensifier and ereunao = to search into, investigate, explore) means to search diligently for something, especially for something hidden like miners engaged in digging for precious metals in the bowels of the earth. This word was first used to tell of a dog sniffing out something with his nose. The Septuagint (Lxx), Greek translation of the OT Hebrew, uses this verb Solomon recording that

"If you seek her as silver, and search (exereunao) for her (referring to wisdom) as for hidden treasures (it was the custom to bury valuables in the ground or in holes in the rocks)." (Pr 2:4)

See a good description of the effort spent in searching the earth for precious metals in Job 28:1-28) What is emphasized is the diligent effort that must be made to obtain wisdom. The tragedy is that too often men show more zeal in acquiring material wealth than spiritual treasures.

The two verbs taken together give emphatic expressing to the earnestness with which enlightenment was sought.

And so we see Peter encouraged his readers by reminding them that the prophets of old eagerly anticipated the great salvation that his readers were experiencing. The prophets did not fully understand this salvation which was perfected when Christ came and gave Himself a sacrifice for our sins...it was then that the grace of God became evident (grace had always been there in the OT but they saw it only thru a mirror dimly) and that with Messiah's appearing, suffering, death & resurrection, that the prophets & all righteous (by their faith) men of old were made perfect (see notes Hebrews 11:39; 11:40).

OT saints only saw salvation (Messiah) from a distance. They were neither fully certain nor secure until Christ came. They trusted in hope (hope in OT often equates with "trust"), looking ahead for a conscience freed from sin, looking to the promise of a New Covenant with a New Heart and a New Spirit dwelling within them. Oh, the privilege of NT saints...now we each can go into God’s presence and we can sit down before Him and, with the apostle Paul, say, “Abba, Father.”

SEEKING TO KNOW WHAT PERSON OR TIME THE SPIRIT OF CHRIST WITHIN THEM WAS INDICATING: eraunontes (PAPMPN) eis tina e poion kairon edelou (3SIAI) to en autois pneuma Christou: (1 Peter 3:18,19; Romans 8:9; Galatians 4:6; 2 Peter 1:21; Revelation 19:10)

Seeking to know (2045) (ereunao the root word of exereunao in the previous verse) means to make thorough examination, to make a careful or thorough effort to learn something. It means to search, examine, investigate, inquire, find out.

Jesus used this same verb (ereunao) to chastise the Jews declaring

You search (ereunao) the Scriptures, because you think that in them you have eternal life; and it is these that bear witness of Me and you are unwilling to come to Me, that you may have life. (Jn 5:39-40)

Verse 11 can be interpreted in one of two ways which accounts for the difference in the translations where NASB translates it as

"what person or time" and NIV has "time and circumstances".

In either event, the present tense of "seeking" pictures the prophets as returning continually to the problem that their predictions created for them. Note for example (Da 12:8,9), where Daniel was told that his words were "sealed till the time of the end." The prophets knew that the Messiah would be coming, but they had no knowledge when he would app ear or what the circumstances of his appearance would be. The Old Testament prophets had predicted that Messiah would experience both suffering and glory. However, they did not understand how His suffering and glory would fit together. It is possible to understand that mystery only after Jesus' earthly ministry.

Ereunao is found 6 times in the NT...

John 5:39 "You search the Scriptures, because you think that in them you have eternal life; and it is these that bear witness of Me;

John 7:52 They answered and said to him, "You are not also from Galilee, are you? Search, and see that no prophet arises out of Galilee."

Romans 8:27 (note) and He who searches the hearts knows what the mind of the Spirit is, because He intercedes for the saints according to the will of God.

1 Corinthians 2:10 For to us God revealed them through the Spirit; for the Spirit searches all things, even the depths of God. (Vincent: "Not, searcheth in order to discover; but of the ever active, accurate, careful sounding of the depths of God by the Spirit.")

1 Peter 1:11 (note) seeking to know what person or time the Spirit of Christ within them was indicating as He predicted the sufferings of Christ and the glories to follow.

Revelation 2:23 (note) 'And I will kill her children with pestilence; and all the churches will know that I am He who searches the minds and hearts; and I will give to each one of you according to your deeds.

Jesus Christ clearly did not come into existence at His incarnation as some cults falsely teach. To the contrary, Peter teaches that the Messiah in the Person of the Holy Spirit (cf see note Romans 8:9), took up temporary residence within the writers of the OT and as explained in his second epistle, enabled them to write very specific, detailed prophecies of His glorious salvation (see notes 2 Peter 1:20; 1:21).

The Messianic prophecies were not the product of the imaginations of the prophets but were communicated by the "Spirit of Christ within them." David for example was conscious of God's Spirit at work in him enabling him to speak under the Spirit's guidance writing

"The Spirit of the LORD spoke by me, and His word was on my tongue." (2Sa 23:2).

Peter emphasizes that the the Holy Spirit is not an impersonal influence, but a personal Being.

Was indicating  (1213) (deloo from delos = manifest) means to make plain by words and thus to declare. It means to make some matter known that was unknown or not communicated previously. It means to show clearly, to signify, to make manifest, visible, clear, or plain and to make known.  When spoken of things past it means to tell, relate or impart information (as in 1Cor 1:11;see note Col 1:18). Although deloo is used most often in reference to declarations through articulate language, it is also used often of any kind of indirect communication. When spoken of things future or hidden, deloo means to reveal, show or bring to light.

Deloo means to make something known by making evident what was either unknown before or what may have been difficult to understand. The imperfect tense in this verse emphasizes repeated action in the past and thus pictures the successive disclosures that the Spirit revealed to the prophets. The Spirit of Christ repetitively set before the prophets very specific truths concerning the coming Messiah, here emphasizing His sufferings and His glories.

Deloo is used 28 times in the Septuagint (LXX) (Ex. 6:3; 33:12; Deut. 33:10; Jos. 4:7; 1 Sam. 3:21; 1 Ki. 8:36; 2 Chr. 6:27; Est. 2:22; Ps. 25:14; 51:6; 147:20; Isa. 42:9; Jer. 16:21; Dan. 2:5f, 9, 11, 16, 23ff, 28ff, 47; 4:18; 7:16). Here are some uses in the  Septuagint (LXX)

Exodus 6:3 and I appeared to Abraham, Isaac, and Jacob, as God Almighty, but by My name, LORD, I did not make Myself known (deloo) to them.

Exodus 33:12 Then Moses said to the LORD, "See, Thou dost say to me, 'Bring up this people!' But Thou Thyself hast not let me know (deloo) whom Thou wilt send with me. Moreover, Thou hast said, 'I have known you by name, and you have also found favor in My sight.'

Esther 2:22 But the plot became known (deloo) to Mordecai, and he told Queen Esther, and Esther informed the king in Mordecai's name.

Psalm 25:14 The secret of the LORD is for those who fear Him, And He will make them know (deloo) His covenant. (Spurgeon's Note)

Psalm 51:6 Behold, Thou dost desire truth in the innermost being, And in the hidden part Thou wilt make me know (deloo) wisdom. (Spurgeon's Note)

Psalm 147:20 He has not dealt thus with any nation and as for His ordinances, they have not known (deloo) them. Praise the LORD! (Spurgeon's Note)

Isaiah 42:9 "Behold, the former things have come to pass, Now I declare new things; Before they spring forth I proclaim (Lxx = deloo = make them known) them to you."

Daniel 2:25 Then Arioch hurriedly brought Daniel into the king's presence and spoke to him as follows: "I have found a man among the exiles from Judah who can make the interpretation known (deloo) to the king!"

Deloo is used 7 times in the NT...

1 Corinthians 1:11 For I have been informed concerning you, my brethren, by Chloe's people, that there are quarrels among you.

1 Corinthians 3:13 each man's work will become evident; for the day will show it, because it is to be revealed with fire; and the fire itself will test the quality of each man's work.

Colossians 1:8 (note) and he also informed us of your love in the Spirit.

Hebrews 9:8 (note)  The Holy Spirit is signifying this, that the way into the holy place has not yet been disclosed, while the outer tabernacle is still standing,

Hebrews 12:27 (note) And this expression, "Yet once more," denotes the removing of those things which can be shaken, as of created things, in order that those things which cannot be shaken may remain.

1 Peter 1:11 (note) seeking to know what person or time the Spirit of Christ within them was indicating as He predicted the sufferings of Christ and the glories to follow.

2 Peter 1:14 (note) knowing that the laying aside of my earthly dwelling is imminent, as also our Lord Jesus Christ has made clear (of something divinely communicated) to me.

AS HE PREDICTED THE SUFFERINGS OF CHRIST AND THE GLORIES TO FOLLOW: promarturomenon (PMPMSN) ta eis Christon pathemata kai tas meta tauta doxas: (sufferings Psalms 22:1-21; 69:1-21; 88:1-18; Isaiah 52:13,14; 53:1-10; Daniel 9:24-26; Zechariah 13:7; Luke 24:25-27,44)  (glories Genesis 3:15; 49:10; Psalms 22:22-31; 69:30-36; 110:1-6; Isaiah 9:6,7; 49:6; Isaiah 53:11,12; Daniel 2:34,35,44; 7:13,14; Zechariah 8:18-21; 14:9