In producing random numbers, subjects typically deviate systematically from statistical randomness. It is considered that these biases reflect constraints imposed by underlying structures and processes, rather than a deficient concept of randomness. Random number generation (RNG) places considerable demands on executive processes, and provides a possibly useful tool for their investigation. A group of patients with Parkinson's disease (PD) and a group of controls were tested on a RNG task, both alone and with a concurrent attention-demanding task (manual tracking). Both groups showed the biases in RNG described previously, including a strong counting tendency and repetition avoidance. Overall RNG performance did not differ between the groups, although differences were found in the counting biases in the patient and control groups, with the controls showing a bias towards counting in twos, and the patients a bias towards counting in ones. The secondary task reversed the bias shown by controls and exacerbated the bias in the patients. A network modulation model may help explain many of the features of RNG. We suggest that naturally biased output from an associative network must be actively suppressed by an attention-demanding, limited-capacity process. This suppression may be disrupted by the pathophysiology of PD and by concurrent tasks. Convergent evidence from various sources is discussed which supports a role of the dorsolateral prefrontal cortex (DLPFC) in this process.