Hint: compute $d$ for the alternate value of $e$ considered. Isn't something rather remarkable? What is the probability that it occurs by chance?

While that is totally immaterial given that $p$ and $q$ are billions-n'-billions times too small to prevent factorization (gross understatement), what if we scaled things? Why would it matter (caution: there are several levels of answer to that later one)?

Facts relevant to this (and many other sensible RSA questions) can be found by combing Dan Boneh's classic Twenty Years of Attacks on the RSA Cryptosystem (in Notices of the AMS, Vol. 46, No. 2, pp. 203-213, 1999).
_{I would have properly cited that followup attempt if it had acknowledged what inspired it.}

Hint: compute $d$ for the alternate value of $e$ considered. Isn't something rather remarkable? What is the probability that it occurs by chance?

While that is totally immaterial given that $p$ and $q$ are billions-n'-billions times too small to prevent factorization (gross understatement), what if we scaled things? Why would it matter (caution: there are several levels of answer to that later one)?

Facts relevant to this (and many other sensible RSA questions) can be found by combing Dan Boneh's classic Twenty Years of Attacks on the RSA Cryptosystem (in Notices of the AMS, Vol. 46, No. 2, pp. 203-213, 1999).
_{^{I might have properly cited that followup attempt if it had acknowledged what inspired it.}}

Hint: compute $d$ for the alternate value of $e$ considered. Isn't something rather remarkable? What is the probability that it occurs by chance?

While that is totally immaterial given that $p$ and $q$ are billions-n'-billions times too small to prevent factorization, what if we scaled things?

Facts relevant to this (and many other sensible RSA questions) can be found by combing Dan Boneh's classic Twenty Years of Attacks on the RSA Cryptosystem (in Notices of the AMS, Vol. 46, No. 2, pp. 203-213, 1999).
_{I would have properly cited Jingjing Wang's followup attempt if it had acknowledged what inspired it}.

Hint: compute $d$ for the alternate value of $e$ considered. Isn't something rather remarkable? What is the probability that it occurs by chance?

While that is totally immaterial given that $p$ and $q$ are billions-n'-billions times too small to prevent factorization (gross understatement), what if we scaled things? Why would it matter (caution: there are several levels of answer to that later one)?

Facts relevant to this (and many other sensible RSA questions) can be found by combing Dan Boneh's classic Twenty Years of Attacks on the RSA Cryptosystem (in Notices of the AMS, Vol. 46, No. 2, pp. 203-213, 1999).
_{I would have properly cited that followup attempt if it had acknowledged what inspired it.}