Federal prosecutors said on Friday that Sam Bankman-Fried, the cryptocurrency mogul who was convicted of masterminding a multibillion-dollar fraud, should receive a prison sentence of 40 to 50 years.

The prosecutors outlined the recommendation in a filing in U.S. District Court in Manhattan. Mr. Bankman-Fried’s sentencing hearing is scheduled for March 28, when Judge Lewis A. Kaplan will decide his fate. He faces a maximum possible penalty of 110 years.

“Justice requires that he receive a prison sentence commensurate with the extraordinary dimensions of his crimes,” the prosecutors said in a 116-page sentencing memo to the judge.

The federal probation department separately recommended a 100-year sentence for Mr. Bankman-Fried, 32, effectively a life sentence. But prosecutors said in the filing that sending him to prison for the rest of his life was not warranted, despite the severity of his crime, because of his relative youth.

In a filing last month, lawyers for Mr. Bankman-Fried argued that he should receive a sentence of no more than six and a half years.

A spokesman for Mr. Bankman-Fried said Friday that a lawyer for him will file a response to the government early next week.

Just 18 months ago, Mr. Bankman-Fried was a high-flying crypto mogul, presiding over the cryptocurrency exchange FTX, a $40 billion business empire. But then FTX collapsed practically overnight, putting him in the cross hairs of law enforcement.

In November, a federal jury in Manhattan convicted Mr. Bankman-Fried of stealing $8 billion from FTX’s customers to finance political contributions, investments in other companies and lavish real estate purchases.

FTX’s implosion and Mr. Bankman-Fried’s subsequent arrest and conviction were seen as a historic nadir for the loosely regulated crypto world.

“The crypto industry might be new,” Damian Williams, the U.S. attorney for the Southern District of New York, said after the verdict, “but this kind of fraud, this kind of corruption, is as old as time.”

Since then, the crypto industry appears to have put Mr. Bankman-Fried’s crimes in the rearview mirror. As he prepares for his sentencing, the prices of most digital assets have soared, with Bitcoin reaching a record high this month.

Prosecutors said in Friday’s filing that a sentence of 40 to 50 years was appropriate given the magnitude of Mr. Bankman-Fried’s fraud and its impact on people around the world, including those who had put some of their retirement money and life savings into FTX.

“The sheer scale of Bankman-Fried’s fraud calls for severe punishment,” prosecutors wrote. “The amount of loss — at least $10 billion — makes this one of the largest financial frauds of all time.”

If Mr. Bankman-Fried is given a light sentence, prosecutors said, there is a real risk that he would carry out some future fraud.

In the sentencing submission, prosecutors included several pages of customer messages sent to Mr. Bankman-Fried on X, formerly Twitter, at the time of FTX’s collapse. In many of the posts, customers expressed anger at not having access to their accounts.

Marc Mukasey, the lawyer Mr. Bankman-Fried hired to prepare for the sentencing, argued in his legal filing that the 100-year sentence recommended by the probation department would be reminiscent of the 150 years given to Bernard Madoff, who pleaded guilty in 2009 to running one of the biggest Ponzi schemes in history. Any comparisons between the two men are inappropriate, Mr. Mukasey said, given “the duration and dollars” involved in Mr. Madoff’s crimes — a 20-year-long fraud that generated $64 billion in paper losses.

The probation department’s recommendation was “barbaric” and “grotesque,” he said.

Mr. Mukasey also pointed out that it took a court-appointed trustee more than 15 years to return roughly $14 billion to Mr. Madoff’s investors. By contrast, the bankruptcy lawyers overseeing FTX’s unwinding have suggested that customers of Mr. Bankman-Fried’s failed exchange are likely to get back all of their money on a relatively fast timeline.

Prosecutors said in their filing that even if customers of FTX got most of their money back, they would have had to wait for more than two years for that to happen. Prosecutors said that “is of little comfort for those victims who needed the money in November 2022.”

In the filing, prosecutors asked Judge Kaplan to also order Mr. Bankman-Fried to forfeit more than $10 billion, which represents the losses and stolen money from his crime. Given the millions of potential victims and the complexity of calculating losses, prosecutors said any money turned over by Mr. Bankman-Fried could be distributed in the FTX bankruptcy.

Judges are not required to follow federal sentencing guidelines. And in imposing a sentence, Judge Kaplan can consider a variety of factors, including Mr. Bankman-Fried’s age, the fact that he is a first-time offender and the potential for him to be rehabilitated.

But one factor that may work against Mr. Bankman-Fried is that he chose to testify at his trial and seemed evasive at times during cross-examination. If Judge Kaplan concludes that Mr. Bankman-Fried testified falsely, he could take that into account in deciding the sentence.

In a column this week in The New York Law Journal, John S. Martin, a former federal judge in Manhattan, criticized “irrationally long sentences” for most fraud and white-collar crime. He said 100-year sentences had had “no impact on crime rates.”

“Let me be clear, Bankman-Fried deserves to be punished,” Mr. Martin wrote. But he added, “Our extremely long prison sentences are one of the reasons the United States has the largest prison population in the world.”