Main Page | See live article | Alphabetical index A Smith number has the same digital sum as its prime factors (with multiplicities). <problem—different digital sums. There are at least three kinds: the simple sum of digits, used infra; the modulo-10 sum of the digits, described here; and the iterated sum (keep doing the first kind of digital sum until a fixed point is reached).> 4=2×2; digital sums, 4=2+2 666=2×3×3×37; digital sums, 6+6+6=2+3+3+3+7=18 1776=2×2×2×2×3×37; digital sums, 1+7+7+6=2+2+2=2+3+3+7=21 There are 29928 Smiths less than a million. It is believed that about 3% of any million consecutive integers are Smith numbers. There are an infinite number of palindromatic Smiths. Consecutive Smith numbers (eg 728, 729; 2964, 2965) are called Smith brothers. It is not known <update?> how many Smith brothers there are. Smith numbers were named by Albert Wilansky of Lehigh University for his brother-in-law Harold Smith, who noticed the property in his phone number (4937775). Ref: Martin Gardner, Penrose Tiles to Trapdoor Ciphers, 1988, p299–300 This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.