LONDON (AP) -- Prince William's wife Kate entered a London hospital Saturday to give birth to their second child, igniting a national wave of anticipation and a last-minute betting spree on the name of the new prince or princess. The baby will be fourth in line to the throne and the fifth great-grandchild of Queen Elizabeth II. In a brief statement, palace officials said the Duchess of Cambridge was admitted at 6 a.m. local time (0500 GMT) Saturday to the exclusive Lindo wing at St. Mary's Hospital, arriving by car with William. The couple's first child, Prince George, was born July 22, 2013 at the same hospital. William, who is on leave from his job as an air ambulance pilot, was at his wife's side in the hospital, as he was for George's birth. Royal officials are not expected to provide any more information until the birth, which will be announced on Twitter and Instagram. That announcement will say what gender the baby is, as well as its weight and the time of birth. Prime Minister David Cameron sent his best wishes in a Twitter message. "The whole country will wish her well," he said. The pending birth and uncertainty about the gender has been a boon for Britain's bookmakers, who say they have received thousands of bets on the newborn's gender and possible name. Betting was part suspended after Saturday's announcement, though wagers were still being placed on a name and other characteristics. "Punters have gone royal baby betting mad and now that Kate has gone into labor, there is a huge scramble to predict the royal baby's gender, name, weight, and hair color amongst other things," Coral spokeswoman Nicola McGeady said. "Tens of thousands of bets are being placed across the nation, sparking one of the biggest gambles we have ever seen on a non-sporting event." Anticipation has been building for days. Kate had told a well-wisher earlier this year that the child was due in the second two weeks of April, kicking off what the tabloid press called the Great Kate Wait. Die-hard royal fans have camped outside the hospital, draped in Union Jack flags and waving festive banners. They have waited patiently on the sidewalk, hoping for a glimpse of the family. The Duke and Duchess sent them luxury pastries and a birthday cake at one point this week -- a mark of gratitude for the fans' wish to share their joy. "I told you it'd be a weekend baby," royal camper Kathy Martin said outside the Lindo Wing. The world's media scrambled into place outside the hospital, waiting for news. The couple has been anxious to avoid the media circus that accompanied George's birth, and camera crews began setting up only after the announcement Saturday morning. Kate will be residing in style. Each en-suite in the private maternity unit has Wifi, satellite television, a radio, a safe, a bedside phone and a refrigerator. The wing also offers a "comprehensive wine list should you wish to enjoy a glass of champagne and toast your baby's arrival." Kate gets a 10 percent loyalty discount, as she had her first child there as well. A suite now costs 6,570 pounds ($10,034) for a one-night stay with normal delivery --or 5,913 pound with Kate's discount. Doctors' fees are extra. The couple has said that they don't know whether the baby will be a boy or a girl. A girl will hold her place in the line of succession, and would be the first to benefit from a change in the law which had always put men ahead of their sisters. Betting ran heavily in favor of the child being a girl, despite the lack of any solid evidence to back that up. All the top bets for the baby's name are for girls. Alice and Charlotte are the clear favorites, followed by Elizabeth, Victoria and Diana -- all names with strong connections to royal tradition. Prince Charles has signaled -- twice -- that he's hoping for a granddaughter, which led some to speculate that Charles had some inside information. But many probably just hope Britain will see a new princess: The monarchy has not welcomed a princess born this high up the line of succession for many years. Princess Anne, Charles' sister, was born third in line in 1950. Princesses Beatrice and Eugenie, the daughters of Prince Andrew and Sarah Ferguson, were fifth and sixth in line at the time of their birth.