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Prime factor pattern in numbers one less than a power of 2

The number $4294967295$ has prime factors $3,5,17,257,\text{and }65537$.

The number is one less than a power of $2$, and its prime factors are all one more than a power of $2$. This made me wonder if this happens for other numbers that are one less than a power of $2$.

$N$ | $2^{N}-1$ | $\text{Prime factors}$
--- | --- | ---
$1$ | $1$ | $-$
$\boldsymbol{2}$ | $\boldsymbol{3}$ | $\boldsymbol{3}$
$3$ | $7$ | $7$
$\boldsymbol{4}$ | $\boldsymbol{15}$ | $\boldsymbol{3,5}$
$5$ | $31$ | $31$
$6$ | $63$ | $3,3,7$
$7$ | $127$ | $127$
$\boldsymbol{8}$ | $\boldsymbol{255}$ | $\boldsymbol{3,5,17}$
$9$ | $511$ | $7,73$
$10$ | $1023$ | $3,11,31$
$11$ | $2047$ | $23,89$
$12$ | $4095$ | $3,3,5,7,13$
$13$ | $8191$ | $8191$
$14$ | $16383$ | $3,43,127$
$15$ | $32767$ | $7,31,151$
$\boldsymbol{16}$ | $\boldsymbol{65535}$ | $\boldsymbol{3,5,17,257}$

It appears that each $N$ that is a power of $2$ gives a $2^N-1$ that has prime factors in a pattern. This pattern continues with the number I first mentioned:

$N$ | $2^{N}-1$ | $\text{Prime factors}$
--- | --- | ---
$2$ | $3$ | $3$
$4$ | $15$ | $3,5$
$8$ | $255$ | $3,5,17$
$16$ | $65535$ | $3,5,17,257$
$32$ | $4294967295$ | $3,5,17,257,65537$

Does this pattern continue indefinitely?