Smith number
Summary
A Smith number is a special type of composite number whose digits have a surprising relationship with its prime factors: the sum of the digits of the number is equal to the sum of the digits of its prime factorization. These numbers were named by mathematician Albert Wilansky after he discovered this property in his brother-in-law Harold Smith’s phone number, $4937775$.
For example, the digits of $4937775$ add up to $42$, which is also the sum obtained from its prime factors ($z3 \times 5 \times 5 \times 65837$). The first Smith numbers in base 10 include $4, 22, 27, 58,$ and $85$. Unlike prime numbers, Smith numbers must be composite, and repeated prime factors are counted multiple times when calculating the digit sum. Mathematicians have studied their properties extensively, and it has been proven that infinitely many Smith numbers exist. Some pairs of consecutive Smith numbers are called “Smith brothers,” adding another interesting pattern to these unusual numbers.
ARTICLE
Summary
A Smith number is a special type of composite number whose digits have a surprising relationship with its prime factors: the sum of the digits of the number is equal to the sum of the digits of its prime factorization. These numbers were named by mathematician Albert Wilansky after he discovered this property in his brother-in-law Harold Smith’s phone number, $4937775$.
For example, the digits of $4937775$ add up to $42$, which is also the sum obtained from its prime factors ($z3 \times 5 \times 5 \times 65837$). The first Smith numbers in base 10 include $4, 22, 27, 58,$ and $85$. Unlike prime numbers, Smith numbers must be composite, and repeated prime factors are counted multiple times when calculating the digit sum. Mathematicians have studied their properties extensively, and it has been proven that infinitely many Smith numbers exist. Some pairs of consecutive Smith numbers are called “Smith brothers,” adding another interesting pattern to these unusual numbers.
ARTICLE
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