What is the subjective prong of the Eighth Amendment analysis?

As to the subjective prong of the Eighth Amendment analysis, prisoners must establish prison officials' "deliberate indifference" to the unconstitutional conditions of confinement. Farmer v. Brennan, 511 U.S. 825, 834 (1994). To demonstrate that a prison official was deliberately indifferent to a serious threat to the inmate's safety, the prisoner must show that "the official [knew] of and disregard[ed] an excessive risk to inmate ... safety; the official must both be aware of facts from which the inference could be drawn that a substantial risk of serious harm exists, and [the official] must also draw the inference." Id. at 837. Mere negligence is insufficient to show a violation of the Eighth Amendment. Id. at 835-36.