For ,
3, ..., the first few are 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, ... (OEIS A020639).

If
is composite then
(Séroul 2000, p. 7), with equality for the square of a prime.

A plot of the least prime factor function resembles a jagged terrain of mountains, which leads to the appellation of "twin peaks"
to a pair of integers such that

Erdős, P.; Lacampagne, C. B.; and Selfridge, J. L. "Estimates of the Least Prime Factor of a Binomial Coefficient." Math.
Comput.61, 215-224, 1993.Séroul, R. "The Lowest
Divisor Function." §8.4 in Programming
for Mathematicians. Berlin: Springer-Verlag, pp. 9-11 and 165-167, 2000.Sloane,
N. J. A. Sequences A020639 and A046027 in "The On-Line Encyclopedia of Integer
Sequences."