Story highlights Police estimate 25,000 gathered in Moscow to protest recent election results

Demonstrators dispute the victory of Prime Minister Vladimir Putin's party

Protester: 'We just want free elections. And that's all. We don't want revolution'

Among the tens of thousands of people happily enduring the freezing temperatures in Moscow's Bolotnaya Square is Alexey, an international lawyer. He tells me he's never protested before.

"I'm not a political person," says Alexey, who asked his full name not be used. "I'm just a simple Russian citizen."

Alexey says the day after Russia's parliamentary elections he asked his friends and colleagues who they voted for. Not one said United Russia. "It was some kind of astonishment for me to understand how a party for whom nobody voted could win the elections," he says.

It was enough to inspire Alexey to protest. His story is not unique. Police estimate 25,000 people gathered in Moscow; protest organizers told the crowd they thought some 80,000 gathered.

There are many in the crowd who until recently chose apathy over politics. But the elections on December 4 changed them. The protesters are demanding an annulment of the election results - which saw Prime Minister Vladimir Putin's United Russia party win 238 seats - and a new vote.

Writer Dmitry Glukhovsky says it was the first time he voted. The experience transformed him into another first time protester. "I decided to try to influence the destiny of my country. I came to the polling station, I cast the ballot and it's stolen," Glukhovsky says.

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Another man in the crowd, Vyacheslav Zhmakin, vents similar feelings.

"I'm a little bit angry because they told me, 'give us free time to hear our positions' and so on. And then 'give us your free time to come and vote'. I see my country does not really need my vote," Zhmakin says.

"So you want new elections. Do you want anything else?" I ask.

"Me personally? No," he replies.

It's another point often repeated by the protesters -- they don't want a revolution. Tamara Mamedova and her friends laugh when I use the R-word. "We just want free elections. And that's all. We don't want revolution," Mamedova says. "We just want our rights back and that's all."

But the protest movement of this Russian winter does appear to have one thing in common with the Arab Spring. Social networks played a vital role in mobilizing these educated, middle class people to stand in the snow and demand political change.

"I think without the Internet, without Facebook and without Russian parallel social network services, this would not have been possible," Glukhovsky says.

Many in this crowd are politically inexperienced. None of them is naive. No one here believes this one gathering will convince Prime Minister Putin to annul the vote and hold new elections. But it has inspired hope and the protesters say that's a profound change.

"I feel one, a union, with all these people," Mamedova says. "I believe we can do something. Something really great that can change the whole political situation in Russia."