  This paper reports the results of a search for first occurrences of
square-free gaps using an algorithm based on the sieve of Eratosthenes. Using
Qgap(L) to denote the starting number of the first gap having exactly the
length L, the following values were found since August 1999:
Qgap(10)=262315467, Qgap(12)=47255689915, Qgap(13)=82462576220,
Qgap(14)=1043460553364, Qgap(15)=79180770078548, Qgap(16)=3215226335143218,
Qgap(17)=23742453640900972 and Qgap(18)=125781000834058568. No gaps longer than
18 were found up to N=125870000000000000.
