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Prime Number s are not considered, since it is obvious that all of them satisfy the condition given above. In base 10, the first few Smith numbers 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, 985, 1086 W.L. McDaniel in 1987 proved that there are infinitely many Smith numbers. There are 29,928 Smith numbers below one million. Practical investigation has shown the density of Smith numbers falling to 2.41% by 1010. There are an infinite number of Palindromic Smith numbers. Consecutive Smith numbers (for example, 728 and 729, 2964 and 2965) are called Smith brothers. It is not known how many Smith brothers there are. The smallest Smith triple is (73615,73616,73617), quads (4463535, 4463536, 4463537, 4463538), quints (15966114,...) and hextuplets (2050918644,...). See {Link without Title} . Smith numbers were named by Albert Wilansky of Lehigh University for his brother-in-law Harold Smith whose phone number (4937775) was the first noticed Smith number. Smith numbers can be constructed from factored Repunit s. The largest known Smith number is ( As Of 2005 ) 9xR1031x(104594+3x102297+1)1476x103913210 where R1031 = 21032-1. EXTERNAL LINKS
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