Tuesday, May 19, 2009

417

417 = 3 x 139.

417 is the smallest integer n such that n, n + 1, n + 2, and n + 3 all have different numbers of distinct prime factors: 417 = 3 x 139; 418 = 2 x 11 x 19; 419 is a prime; 420 = 22 x 3 x 5 x 7.

Inserting a 1 between adjacent digits of 417 produces a prime: 41117.

417 is a number that becomes prime if any digit is deleted: 17, 47, and 41.

Telephone area code 417 serves southwestern Missouri.
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