As the Democratic primary contest for mayor of Philadelphia enters its final month, the conventional wisdom has State Sen. Anthony H. Williams as the front-runner.

Williams and his supporters, however, are discernibly discomfited about the mayor's race.

The thinking goes:

Williams, an African American, will outpace the primary's two other top-tier candidates - both white - with a wave of support from black voters.

Former District Attorney Lynne M. Abraham's strong name recognition won't sustain her campaign if she lacks the financial resources of the outside groups supporting Williams and former City Councilman Jim Kenney.

Kenney's considerable campaign momentum and overwhelming union support won't be enough to defeat a unified black vote.

The other candidates - former State Sen. T. Milton Street Sr., former Common Pleas Court Judge Nelson A. Diaz, and former PGW executive Doug Oliver - will only nibble around the edges of the vote.

Still, Williams is chafing at media coverage, claiming he is being unfairly cast as the candidate who will win only because of the color of his skin.

Though Williams says he rejects the racial math of Philadelphia politics - white voters support white candidates, black voters support black candidates - his supporters are clearly counting on it.

Sulaiman Rahman, founder of the Urban Philly Professional Network and a Williams backer, hosted an event called #BlackVotersMatter last month at the African American Museum.

The event was open to all candidates. The list of guests was heavy with Williams supporters.

A group calling itself the Philadelphia Black Political Coalition held a "Black Political Summit" on April 11 at Dobbins High School. The goal was to develop a "collective black agenda" and then ask the candidates to sign on.

The Philadelphia Community of Leaders, which describes itself as an "African American organization dedicated to addressing the systemic issues facing the African American community," endorsed the summit.

The group also includes many Williams supporters, including Dawn Chavous, his campaign manager; and William Miller IV, a key adviser.

Miller said current efforts to engage and energize black voters hark back to the African American movement in the late 1970s that helped pave the way for W. Wilson Goode Sr. to become the city's first black mayor.

"We've made significant progress, but there's still work to be done," Miller said.

Another member, Bilal Qayyum, who helped organize the summit, suggested there was an effort to split the black vote for mayor.

Qayyum, a longtime community activist, cited as proof the recent endorsement of Kenney by State Rep. Dwight Evans and other black elected officials and ward leaders in the group known as the Northwest Coalition.

"We are the majority block of voters come May 19," Qayyum said. "The black community will decide. That's why all this movement is happening to split the black community."

It's clear those endorsements seriously rattled the Williams campaign.

Miller, joined by other current and former elected officials, called a news conference in Northwest Philadelphia on Thursday to tout Williams for mayor.

There, former Councilman George Burrell predicted white voters in South Philadelphia would support Kenney because they know and trust him.

The black community, Burrell said, should do the same for Williams.

That is the racial math Williams publicly rejects - "One Philadelphia" is his campaign motto - spoken by a Williams supporter.

Three of the city's last four mayors have been African Americans. That means the city has been led by black mayors for 23 of the last 31 years.

The sole white mayor in all that time was Ed Rendell, who ran in 1991 in a racially polarized primary against two black candidates.

Burrell was one of them.

A black state senator who had once run for mayor caused a stir that year by endorsing Rendell.

His name was Hardy Williams. His son now holds his state Senate seat and is running for mayor.

This is what Hardy Williams, who died in 2010, had to say 24 years ago about black political empowerment in the city:

"That chapter started and ended. Now we have the right - just like anybody else - to pick and choose like anybody else."