What is the shortest time it takes to express a gene?

At least in eukaryotes, the shortest protein product that you can translate would be a dipeptide requiring your start codon, a filler amino acid to cause the first translocation step and the stop codon to kick off the ribosome.

As a result a gene would require at least 9 nucleotides.

The smallest known protein, Trp-cage, contains 20 amino acids, so it has, at minimum, a genetic code containing 60 base pairs. However, it is an artificially created protein, so it doesn't really count (it does, however, provide a lower bound on what's possible). There are also tRNA genes, which aren't genes in the normal sense, but rather instructions for constructing tRNAs. The shortest known tRNA gene is 76 base pairs. (I don't think tRNA genes really count, either.)

The shortest known functional gene (that is, it codes for a protein that is actually used by the organism) is a histone gene that is about 500 base pairs long. Histones are proteins that are involved in organizing DNA into nucleosomes, which are the compact basic building blocks of chromosomes.

ooh i like the question. but i would like to know which gene or do you just want general information which is not specific? if yes then tell me and i can help you out.

regards

I think general information would do because it varies widely from organism to organism, gene to gene.