* Front month still well below recent 21-month high * Weather mixed over the nation, cool early in week in East * Nuclear power plant outages remain above average By Eileen Houlihan NEW YORK, May 13 (Reuters) - U.S. natural gas futures edged higher early on Monday, boosted by cool weather early this week in consuming regions in the Northeast despite fairly mild spring weather in most other parts of the nation. Most traders expect the cooldown in the East to be the last stretch of heating demand after a long, cold winter put a huge dent in inventories and a cool spring led to a slow start to the injection season. But forecasts for milder weather in the coming days and weeks should curb any more late-season heating demand before heavy cooling kicks in, helping to increase weekly inventory builds. Still, prices remain well under the recent 21-month high. As of 9:27 a.m. EDT (1327 GMT), front-month June natural gas futures on the New York Mercantile Exchange were at $3.947 per million British thermal units, up 3.7 cents. The contract hit a one-month low of $3.883 last week after climbing to a 21-month high of $4.444 on May 1. The National Weather Service's latest six-to-10-day forecast issued on Sunday called for above-normal temperatures along the West Coast and in the Northeast and mid-Atlantic and below-normal readings along the Gulf Coast stretching into the Plains. Near-normal temperatures were expected for the remainder of the nation. Nuclear plant outages totaled 20,400 megawatts, or 20 percent of U.S. capacity, up from 19,700 MW out on Friday, 17,600 MW out a year ago and a five-year average outage rate of 18,200 MW. ANOTHER LARGE BUILD, BUT STOCKS BELOW NORMAL Last week's gas storage report from the U.S. Energy Information Administration showed domestic inventories rose the prior week by 88 billion cubic feet, above Reuters poll estimates for an 83-bcf build, a year-ago gain of 30 bcf, and the five-year average build of 69 bcf for that week. But inventories, which started the injection season about three weeks later than expected due to the cold spring, are at 1.865 trillion cubic feet, more than 28 percent below last year and 5 percent below the five-year average. Early injection estimates for this week's EIA report range from 87 bcf to 108 bcf, versus a 56-bcf build in the same week last year and a five-year average rise for that week of 83 bcf. Baker Hughes' data on Friday showed the number of rigs drilling for natural gas in the United States slid by four to an 18-year low of 350.