DEMOCRAT REPUBLICAN 60 won 63 lost REPUBLICAN DEMOCRAT 60 won 63 lost DEMOCRAT REPUBLICAN 60 won 63 lost Note: Fifteen moved to runoffs in Texas, which are required if no candidate wins more than 50 percent of the vote. They are not shown in the chart.

Record numbers of women are running for Congress. And many are winning: Ten states have had primaries so far, and in those, 60 women have won and 63 have lost.

But for all the energy, it’s not an easy road to Capitol Hill. There has been a similar surge among men running for office, so the fields are crowded. And the dynamics of races are tough — most women are choosing to run in districts that do not favor them, either in the primary or in the general election in November.

Still, there are opportunities to make history. In Pennsylvania, for instance, which has no women in its 20-member congressional delegation, eight women moved on to the general election from the primaries on Tuesday.

The surge in the number of candidates is mostly among Democrats, and of the 60 candidates who have won so far, 52 are Democrats. But that does not make Democrats more likely to win.

Most of the winners are Democrats in safe Republican districts.

39 in solid and likely Republican districts 18 in solid and likely Democratic districts 1 in a lean Democratic district 2 in lean Republican districts 39 in solid and likely Republican districts 18 in solid and likely Democratic districts 1 in a lean Democratic district 2 in lean Republican districts 39 in solid and likely Republican districts 18 in solid and likely Democratic districts 1 in a lean Democratic district 2 in lean Republican districts

The biggest obstacle to getting an even proportion of women in Congress — they now make up just 20 percent of the total, with 23 women in the Senate and 84 in the House — is that so many women are running in districts that favor the opposite party.

This is particularly true for Democrats. Of the 52 Democrats who have won their primaries, 34 are in districts that are considered solid or likely Republican seats in the general election in November, based on the ratings of three nonpartisan organizations. Just three are Republicans running in districts considered solid or likely Democratic. Those ratings can change, of course, on a whim of news or whiff of scandal.

About half of them face incumbents in November.

33 are challenging an incumbent in the general election 13 are running for an open seat 14 are incumbents running for re-election 33 are challenging an incumbent in the general election 13 are running for an open seat 14 are incumbents running for re-election 33 are challenging an incumbent in the general election 13 are running for an open seat 14 are incumbents running for re-election

Another hurdle for women, though, is incumbency. Historically, incumbents almost always win. And the best opportunities for women to win are in open seats — in 1992, the “Year of the Woman,” the House banking scandal had helped prompt a high number of retirements, and therefore open seats.

More than half of the women who have won primaries so far — 33 out of 60 — will be challenging an incumbent in the fall. None of the women challenging an incumbent in the primary — that is, a member of her own party — have won so far.

Many won the primaries by large margins.

37 won by more than 50 percent of votes 11 won by less than 50 percent of votes 12 uncontested 37 won by more than 50 percent of votes 11 won by less than 50 percent of votes 12 uncontested 37 won by more than 50 percent of votes 11 won by less than 50 percent of votes 12 Uncontested

With so many candidates competing in primaries — 10 candidates in a district has not been unusual this year — candidates can often win with far less than a majority. But 37 of the women who have won so far won by more than 50 percent of the vote.

In Pennsylvania’s Fifth District, for instance, Mary Gay Scanlon won with 28.4 percent of the vote, in a 10-way race that featured six women, more than in any other Democratic primary in the nation.

Mary Gay Scanlon won the Democratic primary in Pennsylvania's Fifth District, a 10-way race which included six women candidates. Michelle Gustafson for The New York Times

Women won big in Pennsylvania, for a change. (When it comes to representation of women, it is not the only one without any women in the House; West Virginia, Nebraska and Idaho also have none.)

But one Republican woman and seven Democrats emerged as general election candidates in the Pennsylvania primaries on Tuesday. Three are in districts that they are favored to win this fall — and in the Fifth District, two women will now compete in the general: Ms. Scanlon and Pearl Kim, who was unopposed in the Republican primary.