Alcohols can be made from alkyl halides, which can be made from alkanes. However $3° > 2° > 1° > 0°$ for alkyl halides synthesis from alkanes. What approach could make an alkane with primary and secondary carbons into only primary alcohols?
Recently a research paper has been published which claims to effectively convert n-alkanes into n-alcohols.
It proposes a quadruple relay catalysis for selective synthesis of n-alcohols from n-alkanes via the following reaction pathway:
The reaction seems to get yields higher than 75%. The paper itself goes into much detail about each catalyst and its role.
The only catch here is that as this is a hydromethylation, you need to start with an alkane which has one carbon less in its chain than the required alcohol.
: Tang, X.; Gan, L.; Zhang, X.; Huang, Z. N-Alkanes to n-Alcohols: Formal Primary C─H Bond Hydroxymethylation via Quadruple Relay Catalysis. Sci. Adv. 2020, 6 (47), eabc6688.