These charts show how quickly bitcoin is growing

As bitcoin soars to all-time highs, the pace of gains is rapidly picking up speed.

For example, it took well over 1,000 days for each leg of bitcoin's climb from a few cents to $1,000, and from $1,000 to $2,000. But since bitcoin topped $2,000 for the first time this May, the digital currency has added each incremental $1,000 to its price in less than 100 days.

Each colored band in the chart below shows how long it took for bitcoin to climb from one psychologically key level to the other. The latest climb from $4,000 to $5,000 only took about 60 days.

Bitcoin is gaining $1,000 at a faster and faster pace

Source: CNBC analysis of CoinDesk data

Bitcoin hit a record high of $5,856.10 Friday, a sixfold increase for the year, according to CoinDesk. The digital currency now has a market capitalization of more than $90 billion.

Many analysts attribute bitcoin's gains this year to a surge of interest from institutional investors, who are betting on the digital currency's future as a store of value or means of payment.

One way to gauge new investor interest is to look at the growth of the "wallets" that digital currency investors use to store their coins. The number of wallets from major wallet company Blockchain.info has nearly doubled to 17.5 million on Thursday from about 9.2 million this time last year.

Another indication that new money is flowing into bitcoin is the relatively muted performance of other digital currencies this week, Chris Burniske, author of "Cryptoassets: The Innovative Investor's Guide to Bitcoin and Beyond," pointed out."The secular bull trend continues."

In the past, investors have sold other digital currencies and used the profits to buy bitcoin.

Market capitalization of all digital currencies except bitcoin (last 7 days)

Source: CoinMarketCap

That said, some other digital currency watchers say the rapid price gains and surge of interest in digital currencies reflects bubble-like behavior.

"The cryptocurrency craze represents some of the most intense financial speculation the world has ever seen," Elliott Prechter of The Elliott Wave Theorist newsletter, told CNBC. "When it reverses, the significantly higher transaction volume associated with bear markets will stall crypto networks, making it nearly impossible for investors to exit while prices collapses. It will be pandemonium."

— CNBC's John Schoen contributed to this report.