Prison violence in England and Wales (for 12 months to March 2016)
Rise compared to the same period of the previous year
2,953 Serious assaults
5,423 Attacks on prison staff
5 Apparent homicides (in 12 months to June 2016)
Source: Ministry of Justice
BBC home affairs correspondent Danny Shaw said he understood the knife used in the attack was "bigger than a Bowie knife but smaller than a machete". It has been recovered.
Mahmoud, who was of Somalian origin, was attacked on the fifth floor landing of one of the prison wings, before being thrown over the railings, falling about 30ft (nine metres).
The motive is not yet clear, although claims about a dispute between gangs or drug debts are being investigated.
Mahmoud was jailed for six years and six months in July as one of two gang members sentenced for hiding a loaded Skorpion machine gun and ammunition in a garden in Enfield.
He was already serving five-and-a-half years for a separate robbery.
BBC home affairs correspondent Daniel Sandford visited the family home of Mahmoud in Enfield where relatives confirmed he was the father of a 10-month-old child.
Mahmoud's cousin Aisha Salah, said: "I blame the prison, it's very disturbing. I just hope that place gets shut down as soon as possible because it's not safe."
John Attard, from the Prison Governors Association, recently worked at the prison as a stand-in governor for the weekend.
"The number of incidents I came across really surprised me," he said.
"We had prisoners fighting that had to be taken to the segregation unit - we retrieved weapons from them. We had drugs coming over the wall that were packed into tools so they could get through the netting."
He said the abuse three officers received when trying to conduct a drug test on a prisoner was something he had never seen before.
The MoJ said: "We are fully committed to addressing the significant increase in violence, self-harm and self-inflicted deaths in our prisons."
It added that it was going to spend an extra £14m in 10 prisons and increase staffing levels by more than 400 prison officers.
Analysis: BBC Home Affairs Correspondent Danny Shaw
Pentonville's Governor Kevin Reilly has noted that in recent weeks people had "felt anxious" about violence at the jail.
Writing in an internal newsletter, seen by BBC News, Mr Reilly said reducing violence was one of his "top five priorities".
He said although there had been a slight reduction in violent incidents during the month, people remained concerned.
In July the Pentonville Independent Monitoring Board said the government should "knock down" or "urgently upgrade" the 174-year-old prison.
The board said the jail was "decrepit" and blamed the former legal high Spice for driving an illicit economy which in turn had led to violence, self-harm and bullying.
In its annual report on Pentonville, the board said there were 16 violent incidents each week but the number had fallen year-on-year.
The Pentonville death is the third killing this year in jails in England and Wales, and the 11th since the start of 2015.
Visitors queuing to see friends and relatives inside the prison spoke of their safety concerns.
"My son is 21. I haven't felt the same since I heard the news," one woman said.
"As a mother everyone tells you at least you know where he is and he is safe - but actually he's not safe, is he?
"No matter their age or what they have done, no-one deserves to die in prison."
The director of the Prison Reform Trust, Peter Dawson, called for fewer people to be sent to jail to "reduce the pressure" on prisons.
"The Victorians thought [Pentonville] could accommodate 900 prisoners... we say it can accommodate up to 1,300.
"That means in practice that almost everybody in a prison like Pentonville can expect to share a cell which the Victorians thought was fit for one person."
In July 2015, the then Justice Secretary Michael Gove said: "Pentonville is the most dramatic example of failure within the prison estate, but its problems, while more acute than anywhere else, are very far from unique,"
A Prison Service spokesman said: "Police are investigating an incident at HMP Pentonville. It would be inappropriate to comment further at this stage."
Category B prison, which means its inmates are believed to pose a high risk to other people, but do not require maximum security
The Victorian jail, in north London, opened in 1842