SARS-CoV-2 infection can lead to acute respiratory syndrome in patients, which can be due in part to dysregulated immune signalling. We analyze here the occurrences of CpG dinucleotides, which are putative pathogen-associated molecular patterns, along the viral sequence. Carrying out a comparative analysis with other ssRNA viruses and within the Coronaviridae family, we find the CpG content of SARS-CoV-2, while low compared to other betacoronaviruses, widely fluctuates along its primary sequence. While the CpG relative abundance and its associated CpG force parameter [1] are low for the spike protein (S) and comparable to circulating seasonal coronaviruses such as HKU1, they are much greater and comparable to SARS and MERS for the 3’-end of the viral genome. In particular, the nucleocapsid protein (N), whose transcripts are relatively abundant in the cytoplasm of infected cells and present in the 3’UTRs of all subgenomic RNA, has high CpG content. We speculate this dual nature of CpG content can confer to SARS-CoV-2 high ability to both enter the host and trigger pattern recognition receptors (PRRs) in different contexts. We then investigate the evolution of synonymous mutations since the outbreak of the COVID-19 pandemic. Using a new application of selective forces on dinucleotides to estimate context driven mutational processes, we find that synonymous mutations seem driven both by the viral codon bias and by the high value of the CpG force in the N protein, leading to a loss in CpG content. Sequence motifs preceding these CpG-loss-associated loci match recently identified binding patterns of the Zinc Finger anti-viral Protein (ZAP) protein.