Mystery surrounds a castaway's claim that he survived for 13 months at sea after what was supposed to be a one-day fishing trip back in 2012. The journey, as he tells it, took him from Mexico to the Marshall Islands. Parts of his story have already checked out, while other questions remain. Here are five things to know about the incredible story of Jose Salvador Alvarenga.

Who is the castaway?

Jose Salvador Alvarenga is a Salvadoran national who had been living in southern Mexico and worked as a fisherman on the Pacific coast.

Officials say that the 37-year-old was an undocumented worker in Mexico.

Photos: Castaway Jose Salvador Alvarenga Photos: Castaway Jose Salvador Alvarenga Castaway Jose Salvador Alvarenga – Jose Salvador Alvarenga attends a news conference in Majuro, Marshall Islands, on Thursday, February 6. Alvarenga, who is from El Salvador, said he spent 13 months lost in the Pacific Ocean, floating from Mexico to the Marshall Islands, which is about halfway between Hawaii and Australia. Hide Caption 1 of 5 Photos: Castaway Jose Salvador Alvarenga Castaway Jose Salvador Alvarenga – Alvarenga is helped up the stairs as he walks to the news conference in Majuro. He returned to a hospital to be intravenously fed, said a top Mexican trade official. Hide Caption 2 of 5 Photos: Castaway Jose Salvador Alvarenga Castaway Jose Salvador Alvarenga – A photo obtained on February 6 shows Alvarenga's boat shortly after his January 30 arrival on Ebon Atoll in the Marshall Islands. Alvarenga says that in December 2012, he and another man set off on a fishing trip from the port of Paredon Viejo, Mexico. He said they were blown off course by winds and then got caught in a storm, losing the use of their engines. Hide Caption 3 of 5 Photos: Castaway Jose Salvador Alvarenga Castaway Jose Salvador Alvarenga – Alvarenga waves as he walks with the help of a nurse in Majuro on Monday, February 3. Alvarenga said his companion died of starvation because he refused to eat raw birds and turtles. Hide Caption 4 of 5 Photos: Castaway Jose Salvador Alvarenga Castaway Jose Salvador Alvarenga – A photograph of a younger Alvarenga, shared by his father, Jose Ricardo Orellana. Hide Caption 5 of 5

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His family in El Salvador has said they had not seen their son in about eight years, and presumed that he was in jail or dead.

According to Alvarenga, he went on a one-day shark fishing trip with a teenage companion, and was caught up in a storm that killed his engine and left him adrift for 13 months.

How long was he supposedly at sea?

By Alvarenga's own account, he was out at sea for 13 months, having left in December 2012.

Local fishermen in the area of Mexico from which he set off say he may have been gone for a month longer than that, which more or less matches a document from a local civil protection agency that reports he disappeared in November 2012.

Officials in the Marshall Islands -- where the bearded, shaggy-haired Alvarenga turned up last Thursday in a heavily damaged boat -- say they've abandoned efforts to pin down the length of time he spent lost in the ocean.

"We gave up on trying to find out the truth of how long he drifted," said Anjanette Kattil for the ministry of foreign affairs. "Time will confirm his story. What we've been concentrating on is his medical condition to see if he's OK, and his repatriation."

How far did he travel?

If Alvarenga's story proves true, the trip would have taken him across roughly 6,600 miles (10,800 kilometers) of open ocean before ending in the archipelago nation, about halfway between Hawaii and Australia in the northern Pacific.

Given the average currents between Mexico and the Marshall Islands, it would have taken less than a year to travel from the origin to the end in the strongest average currents. If the trip did indeed take about 13 months, a meandering journey in and out of the currents was most likely.

Is this even possible?

Alvarenga's claims have garnered widespread skepticism about how he could survive for so long adrift on the Pacific. But from what officials can tell, they have no reason to doubt him.

"The investigations into Mr. Alvarenga's story so far have been substantiated," said Phillip Muller, the Marshall Islands' foreign affairs minister.

Such an amazing journey isn't unheard of, as three Mexican fishermen made a similar drift voyage in 2006 that lasted nine months. Those men lived off fish they caught and rainwater, and they read the Bible for comfort.

It is also notable that other fisherman in the town where he claims to have set sail remember him and have told reporters about their search efforts to find him.

Locals even placed flowers in front of the house where Alvarenga lived, believing he had died.

Shouldn't he be in worse physical shape?

Skeptics point to the meat on Alvarenga's bones as suspicious. If he was stranded for 13 months, wouldn't he be in much worse physical shape?

Alvarenga has said he lived off fish and turtles he had caught and relied on rainwater, and sometimes his own urine, to try to stay hydrated.

And as for his health, it may not be as good as originally thought.

He returned to a hospital to be intravenously fed, said Christian Clay-Mendoza, a top Mexican trade official.

"Doctors say he's severely dehydrated and low on vitamins and minerals," he said.

Doctors said Alvarenga's limbs have started to swell, and they can't seem to keep him hydrated.