
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) In 1982, when Albert Wilansky called his brotherinlaw, he noticed that the phone number was composite and that the sum of the digits in the phone number equals the sum of the digits in its prime factors. 4937775 = 3^{.}5^{.}5^{.}65837Composite numbers with this property are now called Smith numbers after the brotherinlaw Wilansky was calling. Trivially, all prime numbers have this property, so they are excluded. The Smith numbers less than 1000 are: 4, 22, 27, 58, 85, 94, 121, 166, 202, 265, 274, 319, 346, 355, 378, 382, 391, 438, 454, 483, 517, 526, 535, 562, 576, 588, 627, 634, 636, 645, 648, 654, 663, 666, 690, 706, 728, 729, 762, 778, 825, 852, 861, 895, 913, 915, 922, 958, and 985. In 1987, Wayne McDaniel showed that are infinitely many Smith numbers by constructing a sequence of them. If R_{n} is a repunit prime, then 1540^{.}R_{n} is a Smith number (with digital sum 18+n). Note that 1540 is not the only possible mutiplier here, others include: 1540, 1720, 2170, 2440, 5590, 6040, 7930, 8344, 8470, 8920, 23590, 24490, 25228, 29080, 31528, 31780, 33544, 34390, 35380, 39970, 40870, 42490, 42598, 43480, 44380, 45955, 46270, 46810, 46990, 47908, 48790, and 49960.
See Also: EconomicalNumber Related pages (outside of this work)
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Chris K. Caldwell © 19992020 (all rights reserved)
