103 (number)

103 is a prime number, and the largest prime factor of ${\displaystyle 6!+1=721=7\cdot 103}$.^[1] The previous prime is 101. This makes 103 a twin prime.^[2] It is the fifth irregular prime,^[3] because it divides the numerator of the Bernoulli number $${\displaystyle B_{24}=-{\frac {236364091}{2730}}=-{\frac {103\cdot 2294797}{2730}}.}$$

The equation ${\displaystyle 64^{3}+94^{3}=103^{3}+1}$ makes 103 part of a "Fermat near miss".^[4]

There are 103 different connected series-parallel partial orders on exactly six unlabeled elements.^[5]

103 is conjectured to be the smallest number for which repeatedly reversing the digits of its ternary representation, and adding the number to its reversal, does not eventually reach a ternary palindrome.^[6]