# 153

This number is a composite.

153 is equal to the alternating sum and difference of the squares of the integers from 1 to 153's largest prime factor, 17. [Cramer]

π(153) = π(15)*3!. [Gupta]

153 is the sum of all the integers from 1 to 17 (seventeen is prime).

The largest known natural number n such that
2^{n} does not contain the prime
digit 3. It ends with 3, but also with the largest known
prime number (53) with this property. [Capelle]

The sum of the factorial of digits of 153 is prime. [Bajpai]

The smaller member of a Ruth–Aaron pair; since the prime factors of 153 are 3 and 17, and the prime factors of 154 are 2, 7, and 11. Finally, 3 + 17 = 2 + 7 + 11. [Luen]

Smallest number in a set of three consecutive triangular numbers with three prime factors (counted with multiplicity). Note it is the only known number in the sequence which is not squarefree. [Gupta]