Addendum: A typo (an accidental inclusion of the [I]k[/I] term) has been made inadvertently in the previous post #11,
[url]https://www.mersenneforum.org/showpost.php?p=604211&postcount=11[/url].
Therefore, post #11 is concerned only with prime exponents [I]p[/I] = 11, 23, 83, 131, 179, 191, 239, 251, 359, 419, 431, 443, 491, 659, 683, 719, 743, 911, 1019, 1031, 1103, 1223, 1439,..., 999998903, 999999191,..., for which [I]k[/I] = 1.
[B]The statement in post #11 does not hold for [I]k[/I] ≥ 2.[/B]