Mangham had earlier admitted hacking but argued that he only wanted to show Facebook how to improve its security as he had done for Yahoo(Mangham, who had previously been rewarded by Yahoo for finding vulnerabilities in its systems).
Sentencing Mangham, Judge Alistair McCreath said his actions could have been "utterly disastrous" for Facebook.
Alison Saunders, from the Crown Prosecution Service, described the case as "the most extensive and flagrant incidence of social media hacking to be brought before British courts".
Facebook spent $200,000 (£126,400) dealing with Mangham's crime, which triggered a "concerted, time-consuming and costly investigation" by the FBI and British law enforcement, Mr Patel said.
BBC quoted as "A Facebook spokesman" saying: "We applaud the efforts of the Metropolitan Police and the Crown Prosecution Service in this case, which did not involve any compromise of personal user data.
"We take any attempt to gain unauthorised access to our network very seriously and we work closely with law enforcement authorities to ensure that offenders are brought to justice."
