According to local media reports, the suspected bitcoin bandit escaped the prison through a window and somehow made the 95km journey to Iceland's global airport in Keflavik. Police said he travelled under a passport in someone else's name, but was identified via surveillance video.
Police Chief Gunnar Schram told local news outlet Visir that Stefansson did not manage the escape alone, saying: "He had an accomplice".
Details are still unclear but the suspect reportedly escaped early on Tuesday and guards reported him missing only after the flight had already left Keflavik for Arlanda airport north of the Swedish capital, Stockholm.
Stefansson has been in prison since February for being the mastermind of what Icelandic media has called the "big bitcoin heist". Jakobsdóttir has yet to comment on claims she shared a flight with a fugitive.
Authorities still haven't found the stolen computers which are valued at $2 million..
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Stefansson was being held at Sogn prison in rural southern Iceland, 59 miles from the airport.
Police have arrested 22 people altogether, including a security guard, without solving the burglaries. He was moved to the open prison 10 days ago, police said.
Inmates at the prison, which has no fencing, have access to phones and internet.
A professor at the University of Iceland told the LA Times that the "unusual" decision to keep a high-profile suspected criminal like Stefansson at a prison of this nature was rivaled only by "his organized escape".
Iceland's prime minister, Katrín Jakobsdóttir, was reportedly on the same flight as Stefansson on her way to meet India's prime minister in Stockholm on Tuesday. "The underworlds are tiny and it is extremely hard to hide, let alone flee the country".