for some absolute constant and all sufficiently large . Konyagin (1999) subsequently proved the stronger lower bound
where
is an absolute constant and is sufficiently large.
Scheidler and Williams (1992) tabulated up to ,
and Lukes et al. (1997) tabulated for .
The values for ,
2, 3, ... are 3, 6, 7, 7, 23, 62, 143, 44, 159, 46, 47, 174, 2239, ... (OEIS A003458).
Ecklund, E. F. Jr.; Erdős, P.; and Selfridge, J. L. "A New Function Associated with the Prime Factors of ."
Math. Comput.28, 647-649, 1974.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.Granville,
A. and Ramare, O. "Explicit Bounds on Exponential Sums and the Scarcity of Squarefree
Binomial Coefficients." Mathematika43, 73-107, 1996.Konyagin,
S. V. "Estimates of the Least Prime Factor of a Binomial Coefficient."
Mathematika46, 41-55, 1999. https://doi.org/10.1112/S0025579300007555.Lukes,
R. F.; Scheidler, R.; and Williams, H. C. "Further Tabulation of the
Erdős-Selfridge Function." Math. Comput.66, 1709-1717, 1997.Scheidler,
R. and Williams, H. C. "A Method of Tabulating the Number-Theoretic Function
."
Math. Comput.59, 251-257, 1992.Sloane, N. J. A.
Sequence A003458/M2515 in "The On-Line
Encyclopedia of Integer Sequences."
,
for a positive integer 
, is the least integer bigger
than 
such that the least prime factor of 
exceeds 
, where 
is the binomial coefficient (Ecklund et
al. 1974, Erdős et al. 1993). Granville and Ramare (1996) obtained
the lower bound
and all sufficiently large 
. Konyagin (1999) subsequently proved the stronger lower bound
is an absolute constant and 
is sufficiently large.
up to 
,
and Lukes et al. (1997) tabulated 
for 
.
The values for 
,
2, 3, ... are 3, 6, 7, 7, 23, 62, 143, 44, 159, 46, 47, 174, 2239, ... (OEIS A003458).
."
Math. Comput. 59, 251-257, 1992.Sloane, N. J. A.
Sequence