eliminated Sierpiński number candidates

Most numbers $k$ are very easy to eliminate as Sierpiński number candidates, as it is very easy to come up with sequences of primes of the form $k{2}^n+1$. For example, for $k=1$ it is enough to mention the Fermat primes. For some of the seventeen Sierpiński number candidates when the Seventeen or Bust project began, only a single Proth prime, and it is often quite large. Eight candidates remain to be eliminated. The primes listed below were discovered by the Seventeen or Bust project, with the latest being for 19249, discovered by user Konstantin Agafonov of team TSC! Russia.

$k$	Exponent $n$ which gives prime	Prime in base 10 scientific notation
4847	3321063	$1.844857508381060\times {10}^{999743}$
5359	5054502	$2.781168752802502\times {10}^{1521560}$
10223	Still a candidate	N/A
19249	13018586	$1.484360328715661\times {10}^{3918989}$
21181	Still a candidate	N/A
22699	Still a candidate	N/A
24737	Still a candidate	N/A
27653	9167433	$5.727724120920733\times {10}^{2759676}$
28433	7830457	$7.772839072447348\times {10}^{2357206}$
44131	Still a candidate	N/A
46157	Still a candidate	N/A
54767	Still a candidate	N/A
55459	995972	$1.234767571821004\times {10}^{299822}$
65567	1013803	$8.499227304459893\times {10}^{305189}$
67607	Still a candidate	N/A
69109	1157446	$6.366429016367452\times {10}^{348430}$

Title	eliminated Sierpiński number candidates
Canonical name	EliminatedSierpinskiNumberCandidates
Date of creation	2013-03-22 17:21:14
Last modified on	2013-03-22 17:21:14
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	6
Author	PrimeFan (13766)
Entry type	Example
Classification	msc 11A51