Message received from Christophe Clavier, Jan 02 2014:

Here is a list of 14 Brier numbers, all smaller than the smallest Brier number previously known (which was 143665583045350793098657, 24 digits long, discovered in 2007 by Michael Filaseta, Carrie Finch and Mark Kozek).

I computed these numbers on December 31, 2013 and the smallest of them is 3316923598096294713661 which has 22 digits.

Below each number I mention the covering sets related to k.2^n+1 and k.2^n-1 respectively.

43262598580503239091589 (22.6361)
{3, 5, 17, 257, 241, 97, 673}
{61, 41, 11, 31, 151, 331, 37, 13, 73, 19, 7, 3}

107711321583468432196343 (23.0323)
55465536577115049124007 (22.744)
{3, 5, 17, 13, 241, 97, 673}
{61, 41, 11, 31, 151, 331, 37, 109, 73, 19, 7, 3}

105404490005793363299729 (23.0229)
{61, 41, 11, 31, 151, 331, 37, 109, 73, 19, 7, 3}
{3, 5, 17, 13, 241, 97, 673}

3316923598096294713661 (21.5207)
{3, 5, 17, 13, 241, 97, 673}
{1321, 41, 11, 31, 151, 331, 37, 109, 73, 19, 7, 3}

32099522445515872473461 (22.5065)
92348240410439475192041 (22.9654)
50500982247079839441193 (22.7033)
28960674973436106391349 (22.4618)
{61, 41, 11, 31, 151, 331, 37, 109, 73, 19, 7, 3}
{3, 5, 17, 13, 241, 97, 257}

88595984169672153528691 (22.9474)
12607110588854501953787 (22.1006)
10439679896374780276373 (22.0187)
76719416286801468925067 (22.8849)
21444598169181578466233 (22.3313)
{3, 5, 17, 13, 241, 97, 257}
{61, 41, 11, 31, 151, 331, 37, 109, 73, 19, 7, 3}

Smallest Brier number found: 3316923598096294713661 (21.5207)