^
(
	# Find the largest prime factor of N, and capture it in \2
	(?=
		# Repeatedly divide tail by its smallest prime factor until what's left is prime,
		# which will then be captured in \2.
		(
			(xx+)(?=\3+$)     # tail /= {smallest prime factor of tail}
		|
			x*                # Capture the remaining prime
		)+
	)
	# Divide: \4 = N / \2, with \5 = \4-1, enforcing that \5 > 0
	# We can skip the capture of and test for divisibility by \2-1 because \2 is prime.
	(?=
		(                     # \4 = N / \2
			(x+)              # \5 = \4-1
			(?=\2\5*$)
			x
		)
		\4*$
	)
	# Find the next smaller prime than \2 and capture it in \7, with \8 = \7-1
	(?=
		.*(?=\2$).+?
		(?!(xx+)\6+$)
		(x(x*\5))             # Simultaneously capture \7 and enforce that \5 < \7
	)
	# Multiply: tail = \7 * \5
	.*
	(?=\7+$)
	(?=\5\8+$)
)*
xx$