Michael Laird, 39, was found by staff during morning roll check at Whatton Prison, near Nottingham on Sunday.
Prison officers called an ambulance for the man but paramedics pronounced him dead shortly after.
A Prison Service spokesman said Laird, from the Nottingham area, was half way through a six year sentence for making indecent photographs.
He said the Prisons and Probation Ombudsman would now carry out an inquiry.
He added: "Every death in custody is a tragedy and our thoughts are with the family and friends of Mr Laird."
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