In dynamic cognitive radio mesh networks the variation in spectrum diversity and availability is high due to the presence and the sojourn time of primary users. In this research, we develop a Primary Weight Measure (PWM) metric that measures the uniformity of spread of primary users around a particular node. This metric approximates the expected spectral stability and availability around a node. In addition, we consider the stochastic availability of resources in a cognitive radio network environment, and propose a decentralized routing algorithm called Primary Spread Aware Routing Protocol (PSARP). The PSARP is an adaptive per-hop routing scheme that, unlike the predecessor schemes, is nondeterministic. The traffic from a source to a destination is modeled by a Markov process, and packets are forwarded hop by hop based on transition probabilities that reflect the next hop spectral availability as well as the entire path quality. The PWM metrics of the nodes are relayed via back-pressure and are used in the construction of transition probabilities. On a cognitive-based NS2 network simulator, we compare the performance of PSARP with two previously developed routing protocols for dynamic environment. We also develop a Cognitive Stochastic Routing (CSR) protocol based on the PSARP stochastic framework that uses backlogged queue capacity instead of PWM. Our results show higher throughput in PSARP and CSR, which indicate the advantage of stochastic-based routing in a dynamic environment. In addition, PSARP with its PWM measure is more successful in choosing the best path due to the correct identification of the primary users' distribution, and performs substantially better than CSR at high rates.