Does the Bible prophesy that Israel would become a nation again in the twentieth century?

Not directly. What we do know from Luke 21:24-25 is that Jerusalem will be trodden down by the Gentiles until the times of the Gentiles are fulfilled, which the next verse ties to the second coming. So Jerusalem has to exist and will remain under the thumb of the Gentiles until Christ returns; there is no glorious resurrection of Israel dominating the world, that is baloney, Scripture says the opposite. There is also an implication of Israel's existence in Matthew 24, where Jesus says, when you see the fig tree in leaf, know that I am at the very doors. In Matthew and Mark he comes to a fig tree in leaf but with no fruit and says, may you never bear fruit, a personification of faithless Jerusalem, which has been in leaf but fruitless ever since, even after 1948 when the United Nations gave them half of Palestine and the name Israel. Roughly ninety-five percent of the world's Jews still do not believe in Jesus, only a small remnant, just as in his day. So when the fig tree is in leaf again as a nation, it signals that his return is near, though he already told us no one knows the day or the hour.