41

Number
$41$ (forty-one) is:


 * The $13$th prime number, after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37$


 * The $7$th Sophie Germain prime after $2, 3, 5, 11, 23, 29$:
 * $2 \times 41 + 1 = 83$, which is prime.


 * The $5$th of the sequence of $n$ such that $p_n \# - 1$, where $p_n \#$ denotes primorial of $n$, is prime:
 * $3, 5, 11, 13, 41$


 * The $6$th and largest lucky numbers of Euler after $2, 3, 5, 11, 17$:
 * $n^2 + n + 41$ is prime for $0 \le n < 39$.


 * The $1$st prime number which is not the difference between a power of $2$ and a power of $3$.


 * The $6$th integer after $7, 13, 19, 35, 38$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $41^2 = 1681; 16 = 4^2, 81 = 9^2$

Also see

 * Smallest Prime Number not Difference between Power of 2 and Power of 3