In recent years, the number of software vulnerabilities discovered has grown significantly. This creates a need for prioritizing the response to new disclosures by assessing which vulnerabilities are likely to be exploited and by quickly ruling out the vulnerabilities that are not actually exploited in the real world. We conduct a quantitative and qualitative exploration of the vulnerability-related information disseminated on Twitter. We then describe the design of a Twitter-based exploit detector, and we introduce a threat model specific to our problem. In addition to response prioritization, our detection techniques have applications in risk modeling for cyber-insurance and they highlight the value of information provided by the victims of attacks.