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Should Greece and euro zone bet on bitcoin?

With worries over Greece's status in the euro zone leaving some investors wary about the state of the euro, bitcoin wallet company Coinbase is offering to waive fees for customers using the European currency to buy or sell the cryptocurrency.

Coinbase's founder and CEO, Brian Armstrong, told CNBC's "Squawk Alley" that he's seen a fourfold increase in people buying bitcoin across the euro zone in just the last 48 hours.

"The situation in Greece has sparked an interest across the euro zone," Armstrong said, noting that "the numbers out of Greece are relatively small."

"In some ways it's very difficult to get bitcoin there now," he said. "The banks there are already closed."

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Store with Bitcoin sign
Philippe Lopez | AFP | Getty Images

While many defend the euro's stability, including former ECB President Jean-Claude Trichet, others wonder what impact Greece leaving the euro zone could have on the currency.

So far on the year, the euro has fallen nearly 9 percent, and bitcoin has fallen 20 percent in the same time. However, bitcoin spiked 13 percent in the month of June as the Greek debt talks deteriorated. Even then, bitcoin is far off the highs last seen in 2013 when it traded near $1,000. Now, a bitcoin is worth around $250.

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Armstrong remains bullish on the cryptocurrency.

"The potential downside or the cost of one bitcoin is only a couple hundred dollars; if bitcoin continues to grow like we've seen it do over the last couple of years, the potential upside is 1,000 times or more," he said.