The New Hampshire state capital is Concord, which has also been known over time by the names Rumford and Penacook.
On the national people-radar of the United States, New Hampshire is best known as the state with the first primary in the presidential election, the spot with the worst recorded weather at an inhabited location (Mount Washington weather observatory), colorful fall foliage, and a splashy headline killer, Pamela Smart.
Regionally, New Hampshire is known for skiing, no sales or income tax (which may well change due to school funding lawsuits), the lakes region and the NH International Speedway (formerly the Loudon Racetrack) which is still the home of the Loudon Classic, the longest running motorcycle race in the United States.
New Hampshire is host to the Scottish Highland Games, at Loon Mountain in Lincoln (usually the weekend after Labor day). New Hampshire has also registered an official Tartan with the proper authorities in Scotland; this tartan is worn in kilt form by the State Police while they serve their duties in Lincoln during the Games. Because of the high number of attendents to the Games the State Police are quite visible, both for traffic control and to generally to handle the significant increase in population.
Little known facts: New Hampshire boasts the only piece of Interstate Highway that is two-lane (i.e. a single northbound lane and a single southbound lane) with a cobblestone median. This was done to preserve the Old Man on the Mountain, a rock formation visible from Interstate Highway 93 in Franconia.
Speaking of which, the New Hampshire state quarter shows the self same Old Man on the Mountain, which makes it the only US coin with a head on both faces.
Manchester, the largest city in the state, has a main street (Elm Street) which is a dead-end at both ends.
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