103

Number
$103$ (one hundred and three) is:


 * The $27$th prime number


 * The smallest prime number the period of whose decimal expansion is $\dfrac 1 3$ of its maximum length, that is: $34$:
 * $\dfrac 1 {103} = 0 \cdotp \dot 00970 \, 87378 \, 64077 \, 66990 \, 29126 \, 21359 \, 223 \dot 3$


 * The $3$rd prime number after $53, 71$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$.


 * The larger of the $9$th pair of twin primes, with $101$


 * The $21$st happy number after $1$, $7$, $10$, $13$, $19$, $23$, $28$, $31$, $32$, $44$, $49$, $68$, $70$, $79$, $82$, $86$, $91$, $94$, $97$, $100$:
 * $103 \to 1^2 + 0^2 + 3^2 = 10 \to 1^2 + 0^2 = 1$


 * The $37$th odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime
 * $1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $89$, $97$, $101$, $103$, $\ldots$

Also see

 * Period of Reciprocal of 103 is of Third Maximal Length