The synthesis of a short nucleotide polymer using one strand of unwound DNA as a template. The product is usually a RNA molecule between 4-15 nucleotides long that provides a free 3'-OH that can be extended by DNA-directed DNA polymerases. In certain conditions, for example in response to DNA damage, some primases synthesize a DNA primer. [ http://www.ncbi.nlm.nih.gov/pubmed/38492718 http://www.ncbi.nlm.nih.gov/pubmed/11395402 http://www.ncbi.nlm.nih.gov/pubmed/38203225 ]