For the first time in three weeks, first-time unemployment claims rose for the week ending May 21, the Labor department said Thursday. The advance figure for initial claims was 424,000, an increase of 10,000 from the previous week’s revised figure of 414,000. Unemployment applications are above the 375,000 level, which is considered the benchmark for sustainable job growth. However, the four-week moving average, a less volatile number that flattens out week-to-week fluctuations in the data, was 438,500, a decrease of 1,750 from the previous week’s revised average of 440,250. The number of Americans filing for continuing unemployment claims during the week ending May 14 was a seasonally adjusted 3.69 million, a decrease of 46,000 from the preceding week’s revised level of nearly 3.73 million. The four-week moving average was 3.74 million, an increase of 7,750 from the preceding week’s revised average of 3.73 million. The unemployment rate for workers with unemployment insurance was 2.9 percent for the week ending May 14, a decrease of 0.1 percentage point from the prior week. The total number of people claiming benefits in all programs ending May 7 was 7.73 million, a decrease of 196,976 from the previous week. The largest increases in initial claims for that week were in Florida, Georgia, Hawaii, Idaho, and New Mexico. The largest decreases were in Alabama, California, Michigan, New York, and Wisconsin.