A Collection of Brier Numbers

Compiled by Wilfrid Keller

3316923598096294713661	*	22		Dec	2013	Clavier 1
10439679896374780276373	*	23	p	Dec	2013	Ismailescu
11615103277955704975673	*	23			2014	Vantieghem 2
12607110588854501953787	*	23		Dec	2013	Clavier 11
17855036657007596110949	*	23			2014	Vantieghem 3
21444598169181578466233	*	23	p	Dec	2013	Clavier 14
28960674973436106391349	*	23		Dec	2013	Clavier 9
32099522445515872473461	*	23		Dec	2013	Clavier 6
32904995562220857573541	*	23			2014	Vantieghem 4
38410495110832829780407		23		Aug	2023	Wesolowski 4
32099522445515872473461		23			?	Vantieghem 5
43262598580503239091589		23		Dec	2013	Clavier 2
50500982247079839441193		23		Dec	2013	Clavier 8
55465536577115049124007		23		Dec	2013	Clavier 4
56284389701328043058161		23		Aug	2023	Wesolowski 5
64008563165679686026087		23		Aug	2023	Wesolowski 6
65548720000639644141973		23			?	Vantieghem 6
76719416286801468925067		23		Dec	2013	Clavier 13
88595984169672153528691		23		Dec	2013	Clavier 10
92348240410439475192041		23		Dec	2013	Clavier 7
99970730871809953933447		23			?	Vantieghem 7
105404490005793363299729	*	24	p	Dec	2013	Clavier 5
107711321583468432196343		24		Dec	2013	Clavier 3
143665583045350793098657	*	24		Dec	2007	Filaseta
178328409866851219182953	*	24	p	Aug	2017	Wesolowski 7
187651025481288992423069		24		Jun	2026	Gurisatti 29
216644304573327922644547		24		Apr	2026	Gurisatti 10
216644304573327922644547		24		Apr	2026	Gurisatti 11
239365215362656954573813	*	24	p	Aug	2017	Wesolowski 8
378418904967987321998467	*	24	p	Aug	2017	Wesolowski 9
422280395899865397194393	*	24	p	Aug	2017	Wesolowski 10
684998202368425409181617	*	24	p	May	2026	Gurisatti 16
684998202368425409181617	*	24	p	May	2026	Gurisatti 17
971688764763227907612407	*	24		May	2026	Gurisatti 18
971688764763227907612407	*	24		May	2026	Gurisatti 19
474362792344501650476113	*	24	p	Aug	2017	Wesolowski 11
490393518369132405769309	*	24	p	Aug	2017	Wesolowski 12
773553855548262449239841		24		Apr	2026	Gurisatti 8
773553855548262449239841		24		Apr	2026	Gurisatti 9
1057198980466907795111869		25		Apr	2026	Gurisatti 12
1057198980466907795111869		25		Apr	2026	Gurisatti 13
1214959482086111149448681		25		Aug	2017	Wesolowski 9 +
1547374756499590486317191	*	25		Jun	2010	Wesolowski 13
1574659518193293073896953		25		May	2026	Gurisatti 20
1574659518193293073896953		25		May	2026	Gurisatti 21
1651613100316182634822211		25		May	2026	Gurisatti 22
1651613100316182634822211		25		May	2026	Gurisatti 23
1847270240349655900679557		25		Dec	2013	Clavier 4 +
2579882148294177281806591		25		May	2026	Gurisatti 24
2579882148294177281806591		25		May	2026	Gurisatti 25
2681186855821233923845067		25		May	2026	Gurisatti 26
2681186855821233923845067		25		May	2026	Gurisatti 27
3045998278981289844695333		25		May	2026	Gurisatti 28
3045998278981289844695333		25		May	2026	Gurisatti 29 +
3127894363368981760543181	*	25		Jun	2010	Wesolowski 14
3250597248389004053650661		25	p	Apr	2026	Gurisatti 14
3250597248389004053650661		25	p	Apr	2026	Gurisatti 15
3359730632416034895700067		25		May	2026	Gurisatti 30
3359730632416034895700067		25		May	2026	Gurisatti 31
3411390660447661363351183		25		May	2026	Gurisatti 32
3411390660447661363351183		25		May	2026	Gurisatti 33
3440209451231682850413571		25		May	2026	Gurisatti 34
3440209451231682850413571		25		May	2026	Gurisatti 35
3460847921975938031400739		25		May	2026	Gurisatti 36
3460847921975938031400739		25		May	2026	Gurisatti 37
3780564951798029783879299	*	25		Jun	2010	Wesolowski 14 +
3993938085572253363152261		25	p	Apr	2026	Gurisatti 7
4698804227342444902772647		25		May	2026	Gurisatti 38
4698804227342444902772647		25		May	2026	Gurisatti 39
4809415017104834966367641		25		May	2026	Gurisatti 40
4809415017104834966367641		25		May	2026	Gurisatti 41
5202694850496988193834651		25		Dec	2013	Clavier 10 +
5226774293311056510187759		25		May	2026	Gurisatti 42
5226774293311056510187759		25		May	2026	Gurisatti 43
5641881553607576591441731		25		May	2026	Gurisatti 44
5641881553607576591441731		25		May	2026	Gurisatti 45
6414444673509253397716849		25		May	2026	Gurisatti 46
6414444673509253397716849		25		May	2026	Gurisatti 47
6622600723216628068310563		25		Dec	2013	Clavier 9 +
7104760081600566119199041		25		May	2026	Gurisatti 48
7104760081600566119199041		25		May	2026	Gurisatti 49
7381483395473981980941697		25	p	Dec	2013	Clavier 7 +
7438574178639212261363911		25		May	2026	Gurisatti 50
7438574178639212261363911		25		May	2026	Gurisatti 51
7721599323775986659140607		25		May	2026	Gurisatti 52
7721599323775986659140607		25		May	2026	Gurisatti 53
7727749729908084540827981		25		Jun	2026	Gurisatti 29 +
8296577648306367131528381		25		May	2026	Gurisatti 54
8296577648306367131528381		25		May	2026	Gurisatti 55
8407375302278753335851709		25		Dec	2013	Clavier 13 +
8437742201839353828903133		25		May	2026	Gurisatti 56
8437742201839353828903133		25		May	2026	Gurisatti 57
8476043360963969421064757		25		Apr	2026	Gurisatti 2
8476043360963969421064757		25		Apr	2026	Gurisatti 3
8563992700801737350303137		25		May	2026	Gurisatti 58
8563992700801737350303137		25		May	2026	Gurisatti 59
8851693660223009972455379		25		May	2026	Gurisatti 60
8851693660223009972455379		25		May	2026	Gurisatti 61
9075389690161610674154617		25		May	2026	Gurisatti 62
9075389690161610674154617		25		May	2026	Gurisatti 63
12478238019448313802309439		26		May	2026	Gurisatti 11 +
12730125822957388414539541		26		Dec	2013	Clavier 13 +
13993838539925653173907183		26		May	2026	Gurisatti 58 +
14712401771048756833446109		26		Apr	2026	Gurisatti 8 +
14898864008799328493699191		26		Dec	2013	Ismailescu +
15466179896816542233278149		26		Dec	2013	Clavier 6 +
16660680315952294436984989		26		Dec	2013	Clavier 8 +
16821051922323475818733033		26		Dec	2013	Clavier 7 +
19135538077545420450954149		26		Apr	2026	Gurisatti 8 +
20380799788109742413003743		26		Dec	2013	Clavier 4 +
21867705038000924683065281		26		Jun	2010	Wesolowski 1
24155005016816795415535763		26		Jun	2010	Wesolowski 1 +
25310762298500167593455137		26		Aug	2017	Wesolowski 8 +
27465605830487442244017871		26		Apr	2026	Gurisatti 2 +
30902663634162389353963691		26		Jun	2010	Wesolowski 1 +
31657728243146963448750949		26		May	2026	Gurisatti 57 +
33410952839633551971040019		26		Jun	2010	Wesolowski 14 +
34412348054953317639087871		26		Aug	2017	Wesolowski 10 +
36021635193349744064384491		26		Jun	2010	Wesolowski 14 +
36729751049262642658555747		26		Dec	2013	Clavier 9 +
41875470188602051326659657		26		Dec	2013	Clavier 13 +
41931928132340927444560703		26			2014	Vantieghem 2 +
42591108525495107245272707		26		Jun	2010	Wesolowski 14 +
44715355046584306777571327		26		Dec	2013	Clavier 14 +
44930407789418549515219621		26		Dec	2013	Ismailescu +
46262425373218619463738703		26			?	Vantieghem 6 +
47688651855025940312168429		26		Aug	2017	Wesolowski 10 +
47867742232066880047611079		26	p	May	1974	Cohen
48129204788849032391027671		26		Dec	2013	Clavier 8 +
48817622250939158307695947		26		May	2026	Gurisatti 33 +
48937163378402799409887503		26		Dec	2013	Clavier 14 +
50737304657812465528409201		26		May	2026	Gurisatti 57 +
51006077690073636042166393		26		Apr	2026	Gurisatti 9 +
55077600023184308995649129		26		Dec	2013	Ismailescu +
55308810287902446571724689		26		Dec	2013	Clavier 14 +
55627494324090171544158247		26		May	2026	Gurisatti 11 +
56027835008269182767126993		26		May	2026	Gurisatti 21 +
56379508940731789598866159		26		Aug	2017	Wesolowski 12 +
56818071045105745893091261		26		Jun	2010	Wesolowski 14 +
57714000605594257632438649		26		Aug	2017	Wesolowski 7 +
62620453210387029686845321		26		Aug	2017	Wesolowski 10 +
65448396334296195828347119		26		May	2026	Gurisatti 11 +
65661198048429145807163489		26		May	2026	Gurisatti 58 +
66672392170019891639250353		26		Dec	2013	Clavier 11 +
69467708856928398492856129		26		Dec	2013	Clavier 3 +
75364455482576348226255947		26		Jun	2010	Wesolowski 13 +
77084594926519199095808009		26		Aug	2023	Wesolowski 5 +
77290495578708964440412543		26		May	2026	Gurisatti 57 +
78042138117267955387875697		26		Apr	2026	Gurisatti 2 +
80042549870487851489489483		26		May	2026	Gurisatti 57 +
80953681506919138215440657		26		May	2026	Gurisatti 57 +
81528796907153051312194687		26		May	2026	Gurisatti 57 +
82764094973423793861979891		26		Dec	2013	Clavier 6 +
84087895062999632121238489		26		Aug	2017	Wesolowski 12 +
85117008369232795559556427		26		Jun	2010	Wesolowski 1 +
85122778349435073557078429		26		May	2026	Gurisatti 15 +
86275934058413254088508427		26			?	Vantieghem 6 +
87542761410330409402793159		26		Jun	2010	Wesolowski 1 +
88401313000872455560092359		26		May	2026	Gurisatti 57 +
90488619890282191346458871		26		Dec	2013	Clavier 11 +
90629171236810607180553793		26		May	2026	Gurisatti 32 +
94220534437920434129478407		26		Dec	2013	Clavier 13 +
96556427124456405960388201		26		Dec	2013	Clavier 6 +
97143144709938143682039497		26		Dec	2013	Clavier 13 +
98780254337259331152931819		26		Dec	2013	Clavier 9 +
657  derived from the above		27
212502507013238007431486407		27		Apr	2026	Gurisatti 6
396284345867947111538029513		27		Apr	2026	Gurisatti 5
870220033837543850714903473		27		Apr	2026	Gurisatti 1
878503122374924101526292469		27		Jan	2000	Gallot 3

          14 numbers marked with  p  are primes.
          20 numbers with an  *  are reported at OEIS (sequences A076335, A234594 and A180247).
          29 of the listed Brier numbers are covered by two different covering sets.

          An extended list including entries with more than 27 digits is also available.

          A catalogue describing all known basic Brier numbers  k  provides a label characterizing the number and its author, the
          correponding Sierpiński and Riesel coverings, the product  P  of the primes contained in the union of both sets covering
          the Brier number, and the modulus of the associated cycle.

          A  +  sign added to a label means that the number is not a basic one, but part of the respective cycle.

References.

• Daniel Baczkowski, Justin Eitner, Carrie E. Finch, Braedon Suminski and Mark Kozek, Polygonal, Sierpiński, 
  and Riesel Numbers. Journal of Integer Sequences 18 (2015), #15.8.1.
• Pedro Berrizbeitia, J.G. Fernandes, Marcos J. González, Florian Luca and V. Janitzio Mejía Huguet, 
  On Cullen numbers which are both Riesel and Sierpiński numbers. Journal of Number Theory 132 (2012), 2836−2841.
• Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers. 
  Mathematics of Computation 29 (1975), 79−81.
• Michael Filaseta, Carrie Finch and Mark Kozek, On powers associated with Sierpiński numbers, Riesel numbers 
  and Polignac's conjecture. Journal of Number Theory 128 (2008), 1916−1940.
• Michael Filaseta, Jacob Juillerat and Thomas Luckner, Consecutive primes which are widely digitally delicate 
  and Brier numbers. Integers 23 (2023), #A75.
• Yves Gallot, A search for some small Brier numbers. Manuscript, 2000. 
• Dan Ismailescu and Peter Seho Park, On pairwise intersections of the Fibonacci, Sierpiński, and Riesel Sequences. 
  Journal of Integer Sequences 16 (2013), #13.9.8.
• Lenny Jones, Variations on a theme of Sierpiński. Journal of Integer Sequences 10 (2007), #07.4.4.
• Joe McLean, Numbers of the form k · 2ⁿ ± 1, https://irvinemclean.com/maths/robintro.htm. 
• William Paulsen, The prime number maze. The Fibonacci Quarterly 40 (2002), 272−279.
• Carlos Rivera, Problem 29: Brier Numbers. The Prime Puzzles & Problem Connection, https://www.primepuzzles.net. 
• Full names of other researchers. Eric Brier, Christophe Clavier, Emilia Gurisatti, Emmanuel Vantieghem, Arkadiusz Wesolowski. 

Please address questions about this web page to Wilfrid Keller