Final answer:
A patient with symptoms of UTI and prostatitis with urinalysis showing leukocyte esterase and nitrites is most likely infected by Escherichia coli, which is the common pathogen for such infections.
Step-by-step explanation:
A 58-year-old man with fever and lower back pain, as well as a swollen and tender prostate on digital rectal exam, whose urinalysis reveals 100 WBC/hpf, leukocyte esterase, and nitrites, is most likely suffering from a urinary tract infection (UTI) commonly caused by gram-negative bacteria.
Given the urinalysis findings, particularly the presence of nitrites which suggests a bacterium that produces nitrate reductase, the most likely pathogen causing this condition is Escherichia coli (E. coli). E. coli and related bacteria such as Proteus vulgaris and Klebsiella pneumoniae are known to convert nitrate to nitrite, leading to the presence of nitrites in the urine. While other pathogens like Pseudomonas aeruginosa are also capable of causing UTIs, E. coli is by far the most common cause, especially in the case of prostatitis that accompanies UTI symptoms as described in this scenario.