Grepping progressively through large file

I have several large data files (~100MB-1GB of text) and a sorted list of tens of thousands of timestamps that index data points of interest. The timestamp file looks like: ``` 12345 15467 67256 182387 199364 ... ``` And the data file looks like: ``` Line of text 12345 0.234 0.123 2.321 More text Some unimportant data 14509 0.987 0.543 3.600 More text 15467 0.678 0.345 4.431 ``` The data in the second file is all in order of timestamp. I want to grep through the second file using the time stamps of the first, printing the timestamp and fourth data item in an output file. I've been using this: ``` grep -wf time.stamps data.file | awk '{print $1 "\t" $4 }' >> output.file ``` This is taking on the order of a day to complete for each data file. The problem is that this command searches though the entire data file for every line in time.stamps, but I only need the search to pick up from the last data point. Is there any way to speed up this process?