We study the evidence for a connection between active galactic nuclei (AGN) fueling and star formation by investigating the relationship between the X-ray luminosities of AGN and the star formation rates (SFRs) of their host galaxies. We identify a sample of 309 AGN with $10^{41}<L_mathrm{X}<10^{44} $ erg s$^{-1}$ at $0.2 < z < 1.2$ in the PRIMUS redshift survey. We find AGN in galaxies with a wide range of SFR at a given $L_X$. We do not find a significant correlation between SFR and the observed instantaneous $L_X$ for star forming AGN host galaxies. However, there is a weak but significant correlation between the mean $L_mathrm{X}$ and SFR of detected AGN in star forming galaxies, which likely reflects that $L_mathrm{X}$ varies on shorter timescales than SFR. We find no correlation between stellar mass and $L_mathrm{X}$ within the AGN population. Within both populations of star forming and quiescent galaxies, we find a similar power-law distribution in the probability of hosting an AGN as a function of specific accretion rate. Furthermore, at a given stellar mass, we find a star forming galaxy $sim2-3$ more likely than a quiescent galaxy to host an AGN of a given specific accretion rate. The probability of a galaxy hosting an AGN is constant across the main sequence of star formation. These results indicate that there is an underlying connection between star formation and the presence of AGN, but AGN are often hosted by quiescent galaxies.
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