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
121340501064420684282139		24		Jul	2026	Gurisatti 64
128578084173110239005347		24		Jul	2026	Gurisatti 65
138246164022950027768011		24		Jul	2026	Gurisatti 66
143665583045350793098657	*	24		Dec	2007	Filaseta
146975276034675782238011		24		Jul	2026	Gurisatti 67
149013447379687341852319		24		Jul	2026	Gurisatti 68
154270103982012671971943		24		Jul	2026	Gurisatti 69
164699994803024024106289		24		Jul	2026	Gurisatti 70
166809725167325598855941		24		Jul	2026	Gurisatti 71
178328409866851219182953	*	24	p	Aug	2017	Wesolowski 7
179720050742724156784939		24		Jul	2026	Gurisatti 72
181624214916982309945063		24		Jul	2026	Gurisatti 73
186873410340280831706069		24		Jul	2026	Gurisatti 74
187651025481288992423069		24		Jun	2026	Gurisatti 29
202697040086417336623067		24		Jul	2026	Gurisatti 75
204353576730743025838771		24		Jul	2026	Gurisatti 76
210517324441043153316397		24		Jul	2026	Gurisatti 77
216644304573327922644547	×	24		Apr	2026	Gurisatti 10
216644304573327922644547		24		Apr	2026	Gurisatti 11
228180541442846342379871		24		Jul	2026	Gurisatti 78
239127824894160182970257		24		Jul	2026	Gurisatti 79
239365215362656954573813	*	24	p	Aug	2017	Wesolowski 8
251874502785445808818369		24		Jul	2026	Gurisatti 80
260443204857549946598369		24		Jul	2026	Gurisatti 81
268191405132355466199329		24		Jul	2026	Gurisatti 82
276728598313898441752427		24		Jul	2026	Gurisatti 83
286665538680233820585739		24		Jul	2026	Gurisatti 84
288714474441815685481147		24		Jul	2026	Gurisatti 85
290536818816694480102691		24		Jul	2026	Gurisatti 86
295205579756054452406191		24		Jul	2026	Gurisatti 87
304245623760762252368837		24		Jul	2026	Gurisatti 88
310679261630679716865641		24		Jul	2026	Gurisatti 89
330972312618629688954359		24		Jul	2026	Gurisatti 90
331620285684443656047187		24		Jul	2026	Gurisatti 91
350826607784942503209529		24		Jul	2026	Gurisatti 92
362798963982627909206293		24		Jul	2026	Gurisatti 93
377092172044873248103219		24		Jul	2026	Gurisatti 94
378418904967987321998467	*	24	p	Aug	2017	Wesolowski 9
385096496298282671755961		24		Jul	2026	Gurisatti 95
388310667219502982565529		24		Jul	2026	Gurisatti 96
405412415234979082404601		24		Jul	2026	Gurisatti 97
412266098187888914053481		24		Jul	2026	Gurisatti 98
422280395899865397194393	*	24	p	Aug	2017	Wesolowski 10
424937573181141461982397		24		Jul	2026	Gurisatti 99
426233969994120752175601		24		Jul	2026	Gurisatti 100
426715657068421286076053		24		Jul	2026	Gurisatti 101
431929413275599300580819		24		Jul	2026	Gurisatti 102
432416851722094036490801		24		Jul	2026	Gurisatti 103
437784103807700641783963		24		Jul	2026	Gurisatti 104
439285867254694570526639		24		Jul	2026	Gurisatti 105
445320662244812413533157		24		Jul	2026	Gurisatti 106
446163998103085423901711		24		Jul	2026	Gurisatti 107
458999865117623617260283		24		Jul	2026	Gurisatti 108
460149875576056135526869		24		Jul	2026	Gurisatti 109
472511292118092770814823		24		Jul	2026	Gurisatti 110
473071091495604107045569		24		Jul	2026	Gurisatti 111
474362792344501650476113	*	24	p	Aug	2017	Wesolowski 11
484712250275659308681167		24		Jul	2026	Gurisatti 112
485209626791176101281749		24		Jul	2026	Gurisatti 113
490393518369132405769309	*	24	p	Aug	2017	Wesolowski 12
493727793593943772583063		24		Jul	2026	Gurisatti 114
497505616842367511471629		24	p	Jul	2026	Gurisatti 115
500857467208008883279673		24		Jul	2026	Gurisatti 116
508482120923387467347061		24		Jul	2026	Gurisatti 117
525333868833277503792427		24	p	Jul	2026	Gurisatti 118
566259011294144228421577		24		Jul	2026	Gurisatti 119
569935404732274381780061		24		Jul	2026	Gurisatti 120
570914020159054697029453		24		Jul	2026	Gurisatti 121
580682515651071697748987		24		Jul	2026	Gurisatti 122
594328709774569435829717		24		Jul	2026	Gurisatti 123
596826371144767591830427		24		Jul	2026	Gurisatti 124
616220977578847774768069		24		Jul	2026	Gurisatti 125
617657354031401436939133		24		Jul	2026	Gurisatti 126
619863752900623516848137		24		Jul	2026	Gurisatti 127
625474875614749940829799		24		Jul	2026	Gurisatti 128
630083537656138267926629		24		Jul	2026	Gurisatti 129
631409408839135195993331		24		Jul	2026	Gurisatti 130
632579599817265216614167		24		Jul	2026	Gurisatti 131
632792441876786034028403		24		Jul	2026	Gurisatti 132
634253988328243908338321		24		Jul	2026	Gurisatti 133
634630847361921543357929		24		Jul	2026	Gurisatti 134
635785880730894969644837		24		Jul	2026	Gurisatti 135
638068155003418653981601		24		Jul	2026	Gurisatti 136
641334919017865082324477		24		Jul	2026	Gurisatti 137
645657008892481653394183		24		Jul	2026	Gurisatti 138
659551596038942459788343		24		Jul	2026	Gurisatti 139
665451545069831122759549		24		Jul	2026	Gurisatti 140
666766264021887841041569		24		Jul	2026	Gurisatti 141
667416192939208795777997		24		Jul	2026	Gurisatti 142
684998202368425409181617	×	24	p	May	2026	Gurisatti 16
684998202368425409181617		24		May	2026	Gurisatti 17
693289348129683360717401		24		Jul	2026	Gurisatti 143
706608850779471804878723		24		Jul	2026	Gurisatti 144
721326105653931699528613		24		Jul	2026	Gurisatti 145
721339404270972007966519		24		Jul	2026	Gurisatti 146
733469170138220017604477		24		Jul	2026	Gurisatti 147
739337298871680503980543		24		Jul	2026	Gurisatti 148
752136949667658645924853		24		Jul	2026	Gurisatti 149
755956495861706541990799		24		Jul	2026	Gurisatti 150
758317555376905024458613		24		Jul	2026	Gurisatti 151
767752373978607801878273		24	p	Jul	2026	Gurisatti 152
768297745420245431383061		24		Jul	2026	Gurisatti 153
773553855548262449239841	×	24		Apr	2026	Gurisatti 8
773553855548262449239841		24		Apr	2026	Gurisatti 9
784552836292559780361583		24		Jul	2026	Gurisatti 154
787627437611836135815553		24		Jul	2026	Gurisatti 155
788647020876602456551811		24	p	Jul	2026	Gurisatti 156
830365647124271654961863		24		Jul	2026	Gurisatti 157
834710943643244010295283		24		Jul	2026	Gurisatti 158
845614910203141892230829		24		Jul	2026	Gurisatti 159
852034486034178472955009		24		Jul	2026	Gurisatti 160
856752424683380153271367		24		Jul	2026	Gurisatti 161
864542316513948128359327		24		Jul	2026	Gurisatti 162
872752066637539973312081		24		Jul	2026	Gurisatti 163
872786653774706019074953		24		Jul	2026	Gurisatti 164
890137544528789964530911		24		Jul	2026	Gurisatti 165
891787784176673691127603		24		Jul	2026	Gurisatti 166
892406277196147880759459		24		Jul	2026	Gurisatti 167
892571227008583036539263		24		Jul	2026	Gurisatti 168
901118514445783358732563		24		Jul	2026	Gurisatti 169
913579236253208766873167		24		Jul	2026	Gurisatti 170
915375964032680542504403		24		Jul	2026	Gurisatti 171
918527702635742167120667		24		Jul	2026	Gurisatti 172
929467741479030653456839		24		Jul	2026	Gurisatti 173
950707619800673674043219		24		Jul	2026	Gurisatti 174
959772424362502796727967		24		Jul	2026	Gurisatti 175
969165139600805921889859		24		Jul	2026	Gurisatti 176
969751760658517941856079		24	p	Jul	2026	Gurisatti 177
971688764763227907612407	×	24		May	2026	Gurisatti 18
971688764763227907612407		24		May	2026	Gurisatti 19
973933249145550770620361		24		Jul	2026	Gurisatti 178
980124509664153305937319		24		Jul	2026	Gurisatti 179
988384460177724339396673		24		Jul	2026	Gurisatti 180
989106620501688576798481		24		Jul	2026	Gurisatti 181
998221014805870527576739		24		Jul	2026	Gurisatti 182
1057198980466907795111869	×	25		Apr	2026	Gurisatti 12
1057198980466907795111869		25		Apr	2026	Gurisatti 13
1214959482086111149448681		25		Aug	2017	Wesolowski 9 +
1401207360583113324446743		25		Jul	2026	Gurisatti 73 +
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		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
9510525432652622482396189		25		Jul	2026	Gurisatti 67 +
11492957719938374865634591		26		Jul	2026	Gurisatti 67 +
12478238019448313802309439		26	p	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 +
18220736280916558562707129		26		May	2026	Gurisatti 45 +
19135538077545420450954149		26		Apr	2026	Gurisatti 8 +
20380799788109742413003743		26		Dec	2013	Clavier 4 +
21732194678685286453435621		26		May	2026	Gurisatti 52 +
21867705038000924683065281		26		Jun	2010	Wesolowski 1
21936374453989957751067253		26		May	2026	Gurisatti 54 +
24155005016816795415535763		26		Jun	2010	Wesolowski 1 +
25310762298500167593455137		26		Aug	2017	Wesolowski 8 +
26088029507431589493510653		26		May	2026	Gurisatti 45 +
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 +
47851333295754523871495129		26		May	2026	Gurisatti 59 +
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 +
78802094335245955422959813		26		May	2026	Gurisatti 60 +
80042549870487851489489483		26		May	2026	Gurisatti 57 +
80953681506919138215440657		26		May	2026	Gurisatti 57 +
81528796907153051312194687		26		May	2026	Gurisatti 57 +
82506679750574129705125859		26		May	2026	Gurisatti 39 +
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 +
90084593007198759813175441		26		May	2026	Gurisatti 45 +
90488619890282191346458871		26		Dec	2013	Clavier 11 +
90565899966003865748445883		26		Jul	2026	Gurisatti 70 +
90629171236810607180553793		26		May	2026	Gurisatti 32 +
94220534437920434129478407		26		Dec	2013	Clavier 13 +
94422413153752025277450181		26		May	2026	Gurisatti 59 +
94726870175747821431155149		26		May	2026	Gurisatti 49 +
95013514322638972222689503		26		Jul	2026	Gurisatti 67 +
96556427124456405960388201		26		Dec	2013	Clavier 6 +
96884801078734359903169367		26		Jul	2026	Gurisatti 73 +
97143144709938143682039497		26		Dec	2013	Clavier 13 +
98780254337259331152931819		26		Dec	2013	Clavier 9 +
796  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

          22 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,
               they are marked with an  ×  and reported at OEIS A395816.

          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