A Texas man accused of operating a Ponzi scheme involving bitcoins pleaded guilty on Monday in what prosecutors say was the first U.S. criminal securities fraud case related to the digital currency.

Trendon Shavers, who authorities said defrauded investors after raising more than $4.5 million worth of bitcoins while operating Bitcoin Savings and Trust, pleaded guilty in Manhattan federal court to one count of securities fraud.

"I know what I did was wrong, and I'm very sorry," Shavers said in court.

Under a plea deal, Shavers has agreed not to appeal any sentence at or below 41 months in prison. Sentencing before U.S. District Judge Lewis Kaplan is scheduled for Feb. 3.

Shavers, who went by "pirateat40" online, was arrested in November, two months after a federal judge in Texas ordered him to pay $40.7 million in a related U.S. Securities and Exchange Commission civil lawsuit.

Prosecutors said Shavers, who turned 33 on Monday, raised at least 764,000 bitcoins worth more than $4.5 million based on the average price of bitcoin during the period of the scheme from investors from September 2011 to September 2012. He promised interest rates of 7 percent per week or 3,641 percent a year.

The indictment said Shavers solicited the investments on the website Bitcoin Forum, offering to pay interest to investors who loaned bitcoins to Bitcoin Savings and Trust while he pursued a market arbitrage strategy.

Michael Ferrara, a prosecutor, in court on Monday said Shavers had invested some of the bitcoins with Mt. Gox, the now-defunct Tokoyo-based bitcoin exchange.

But Ferrara said Shavers, who lived in McKinney, Texas, largely instead used new investors' bitcoins to pay back prior investors.

"In other words, he had the telltale signs of a Ponzi scheme," Ferrara said.