Idaho prosecutors explained in detail how they came to believe it was the DNA of student murders' suspect Bryan Kohberger that they recovered from a knife sheath near the body of Madison Mogen in November.

Once they had a cheek swab, they found a "statistical match."

"A traditional STR DNA comparison was done between the STR profile found on the Ka-Bar knife sheath and Defendant’s DNA," prosecutors revealed in court filings this week. "The comparison showed a statistical match."

Mogen, 21, and three friends, Kaylee Goncalves, 21, Xana Kernodle, 20, and Ethan Chapin, 20, were all stabbed to death during a 4 a.m. home invasion, according to court documents.

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Bryan Kohberger listens to arraignment proceedings

Bryan Kohberger, who is accused of killing four University of Idaho students in November 2022, listens during his arraignment hearing in Latah County District Court, Monday, May 22, 2023, in Moscow, Idaho. (Zach Wilkinson/Moscow-Pullman Daily News via Pool)

Local police in Moscow, Idaho, quickly enlisted the help of state police and the FBI, who through a massive effort under blistering public scrutiny tracked their suspect to the other side of the country, where he was celebrating the holidays with his family in Pennsylvania’s Pocono Mountains as four West Coast families grieved the loss of their young adult children.

A comparison of the knife sheath DNA to the FBI’s database came up empty.

Read the prosecutors' filing (Mobile users go here):

Police began using relatively new and publicly available investigative genetic genealogy techniques, according to the court documents. The FBI began checking the sample against publicly available DNA databases and subscription-only archives exclusive to law enforcement, according to the filing.

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Idaho victims last photo

Madison Mogen, top left, smiles on the shoulders of her best friend, Kaylee Goncalves, as they pose with Ethan Chapin, Xana Kernodle, and two other housemates in Goncalves' final Instagram post, shared the day before the four students were stabbed to death. (@kayleegoncalves/Instagram)

Investigators also dug into social media, vital records and pursued leads.

Ultimately, investigators developed a lead and collected a DNA sample from the trash outside the Kohbergers’ home. They found a familial match, and after arresting the 28-year-old criminologist on Dec. 30, collected samples directly from the suspect.

"The STR profile is at least 5.37 octillion times more likely to be seen if Defendant is the source than if an unrelated individual randomly selected from the general population is the source," prosecutors explained in court filings.

Bryan Kohberger Prosecutor speaks Kohberger's lawyer

Latah County Prosecutor Bill Thompson speaks with public defender Anne Taylor during an arraignment hearing for Bryan Kohberger, who is accused of killing four University of Idaho students in November 2022, in Latah County District Court, Monday, May 22, 2023, in Moscow, Idaho. (Zach Wilkinson/Moscow-Pullman Daily News via Pool)

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STR, or short tandem repeat, is a common type of DNA testing used in criminal cases, according to the National Institute of Justice, which says an STR match "can give nearly irrefutable evidence statistically of a person's identity."

The revelations came in a motion for a protective order in response to Kohberger's attempts for more discovery materials.

Kohberger’s trial on four charges of first-degree murder was scheduled to begin on Oct. 2. He is being held without bail and could face the death penalty if convicted.