OP: In 1 Corinthians 15:1-4, Paul states the Gospel that saves: that Jesus died for our sins, was buried, and rose again on the third day.
Good question about what exactly is the Gospel?
For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: 1 Cor 15:3-4
There are basically three parts to the whole gospel.
Christ died for our sins.
He was buried.
He rose again the third day.
Paul says this is all according to the scriptures.
How important is this? Very, for Paul it is by which ye are saved.
Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. v 1-2
Christ died for our sins.
This had been prophesied since Genesis.
And then subsequently, including Isaiah.
Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted. But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all. ... Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. He [God] shall see of the travail of his [Christ] soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Isa 53:5-6, 10-11
The word "iniquity" means sin, a depraved action, a crime. (Gesenius)
"Justify" means to be righteous, straight. (Gesenius)
So, the this first part of the gospel is Christ bore our sins by the which God was satisfied and we may be righteous. Between bearing sins and being justified are the other two pieces.
He was buried.
The swoon theory and the stolen body theory persist to this day, but no, the gospel account prophesied He was dead and buried.
And he made his grave with the wicked, and with the rich in his death; because he had done no violence, neither was any deceit in his mouth. Isa 53:9
But God will redeem my soul from the power of the grave: for he shall receive me. Selah. Psalm 49:15
A sin offering is wholly dead.
He rose again the third day.
This too is necessary. Obviously, many people believe Jesus existed, but was simply a man, simply a prophet, or simply something worse. But rising from the dead is simply something else.
Like the other two beliefs, this third of three is also prophesied.
I will ransom them from the power of the grave; I will redeem them from death: O death, I will be thy plagues; O grave, I will be thy destruction: repentance shall be hid from mine eyes. Hos 13:14
Now the LORD had prepared a great fish to swallow up Jonah. And Jonah was in the belly of the fish three days and three nights. Jon 1:3
Conclusion
Without each part of the triad, we lose something that is the gospel.
Christ died for our sins. Once. Never to be repeated.
For in that he died, he died unto sin once: but in that he liveth, he liveth unto God. Rom 6:10
He was buried. He didn't faint or hide or something else.
He rose on the third day.
Can any part be removed, not believed, and still be saved? Which part is unnecessary? Died for our sins, was buried, rose on the third day. Each must be believed as prophesied.
