RECORDS IN COMBINATORICS AND NUMBER THEORY

  • The number of non isomorphic posets with N elements

    P(0) = 1
    P(1) = 1
    P(2) = 2
    P(3) = 5
    P(4) = 16
    P(5) = 63
    P(6) = 318
    P(7) = 2.045 (J.Wright 1972)
    P(8) = 16.999 (S. K. Das 1977)
    P(9) = 183.231 (R. H. Mohring 1984)
    P(10) = 2.567.284 (J. C. Culberson, G. J. E. Rawlins 1990)
    P(11) = 46.749.427 (J. C. Culberson, G. J. E. Rawlins 1990)
    P(12) = 1.104.891.746 (C. Chaunier, N. Lygeros 1991)
    P(13) = 33.823.827.452 (C. Chaunier, N. Lygeros 1992)
    P(14) = 1.338.193.159.771 (N. Lygeros, P. Zimmermann 2000)
    For more information see sequences or references.

  • N consecutive primes in arithmetic progression

    N = 5 (W.J. Blundon, M.F. Jones, M. Lal 1967)
    N = 6 (L. J. Lander, T. R. Parkin 1967)
    N = 7 (H. Dubner, H. Nelson 08/1995)
    N = 8 (H. Dubner, T. Forbes, N. Lygeros, M. Mizony, P. Zimmermann 11/1997)
    N = 9 (H. Dubner, T. Forbes, N. Lygeros, M. Mizony, P. Zimmermann 01/1998)
    Helpers : Quercia (26), Nicholson, Gorham et Mulholland (5.2), Heylen (4.5), Banderier (3.5), Sunde (3.5), Ballinger (3.4), Landreau (3.4), R. Dubner (3.2), Metzner (3.2), Beard (3), Wehmeier (3), Toplic (3), Kierkegaard (2.9), Stevenson (2.5), Biavati (2), Briggs (2), Canart (2), Bronson (1.5), Fauque (1.5), Ketner (1.5), Weiner (1.5), B. et T. Butka (1.4), Taeschner (1.2), Sandbakken (1.2), Rossi (1.2), Buddenhagen (1), O'Hare (1), Peterson (1), Nebe (1), Ruescher (1), Tholberg (1) and Alm, Aschenbrenner, Backhouse, Bell, Bernhard, Berry, Bonacina, Bonn, Clark, Davis, Cohen, Cook, Delepine, Dijkhof, Edge, Erra, Geovanis, Grabysz, Groleau, Gulbrandsen, Hall, Hogan, Jaxon, Kluk, Kriesel, Lamiral, Leunissen, Leong, Leong, Muller, Nastos, Neely, Nunes, Olsen, Polster, Schell, Schroeder, Smart, Smith, Spagnesi, Speare, Svallmark, Trevisan, Weinfurtner, Welsh, Wendling, Womack, Yeackley, Zapata.

    N =10 (H. Dubner, T. Forbes, N. Lygeros, M. Mizony, H. Nelson, P. Zimmermann 03/1998)
    Helpers : Piche (6.0), Heylen (4.76), Toplic (4.25), Kierkegaard (3.0), Erra (2.38), J. Lygeros (1.5), Delepine (1.5), Ketner (1.01), Sandbakken (1.0),Taeschner (0.73), Leunissen (0.70), Fauque (0.68), Zapata (0.66), Ballinger (0.58), Helling (0.51) Backhouse (0.50) and Adrian, Alm, Angrist, Aschenbrenner, Banderier, Belshoff, Berkhout, Bernhard, Bosser, Bray, Brown, Carlin, Colligan, Cors, La Curan, Dwyer, Graham, Groleau, Hali, Hogan, Hyvnen, Johannesdal, Johnson, Kibel, Kidd, Kluk, Kotsireas, Kultala, Kriesel, Kveps, Lamiral, Langlois, Megyesi, Olathe, Olly, Palka, Pedersen, Pinch, Pnisch, Pretti, Rasinen, Richard Richter, Sadoway, Serre, Spagnesi, Szeptycki, Tanative4, Thomas, Turner, Valdes, Joe W. W., Welsh, Weyhaupt.

  • Large Factors Found By Elliptic Curve Method

    Champion of 40 digits
    1232079689567662686148201863995544247703 p(11279) (Lenstra-Dixon 10/1991)
    Champion of 42 digits
    184976479633092931103313037835504355363361 10,201- (D. Rusin 04/1992)
    Champion of 43 digits
    5688864305048653702791752405107044435136231 p(19997) (Berger-Mueller 03/1993)
    Champion of 44 digits
    27885873044042449777540626664487051863162949 p(19069) (Berger-Mueller 06/1995)
    Champion of 47 digits
    12025702000065183805751513732616276516181800961 5,256+ (P. Montgomery 11/1995)
    28207978317787299519881883345010831781124600233 30,109- (P. Montgomery 02/1996)
    Champion of 48 digits
    662926550178509475639682769961460088456141816377 24,121+ (R. P. Brent 10/1997)
    Champion of 49 digits
    1078825191548640568143407841173742460493739682993 2,1071+ (P. Zimmermann 06/1998)
    Champion of 53 digits
    53625112691923843508117942311516428173021903300344567 2,677- (C. Curry 09/1998)
    Champion of 54 digits
    484061254276878368125726870789180231995964870094916937 (N. Lygeros, M. Mizony 12/1999)
    For more information see champions, ecmnet, top100.

  • First Erdös-Woods Numbers.

    For d<=520 see Cégielski and al.
    16,22,34,36,46,56,64,66,70,76,78,86,88,92,94,96,
    100,106,112,116,118,120,124,130,134,142,144,146,154,160,162,186,190,196,
    204,210,216,218,220,222,232,238,246,248,250,256,260,262,268,276,280,286,288,292,296,298,
    300,302,306,310,316,320,324,326,328,330,336,340,342,346,356,366,372,378,382,394,396,
    400,404,406,408,414,416,424,426,428,430,438,446,454,456,466,470,472,474,476,484,486,490,494,498,
    512,516,518,520,526,528,532,534,536,538,540,546,550,552,554,556,560,574,576,580,582,584,590,
    604,606,612,616,624,630,634,636,640,650,666,668,670,

  • Consecutive Erdös-Woods Numbers.

    N=2: 34,36
    N=3: 92,94,96
    N=4: 216,218,220,222 (P. Cégielski, D.Richard 2000)
    N=5: 532,534,536,538,540 (P. Cégielski, D.Richard 2000)
    N=6: 1834,1836,1838,1840,1842,1844 (N. Lygeros 2001)
    N=7: 2166,2168,2170,2172,2174,2176,2178 (N. Lygeros 2001)
    N=8: 4312,4314,4316,4318,4320,4322,4324,4326 (N. Lygeros 2001)
    N=9: 4032,4034,4036,4038,4040,4042,4044,4046,4048 (N. Lygeros 2001)
    For more information see Erdös-Woods Project and Sloane's sequence.

  • Circle orders and SSU conjecture.

    N=07 : (N. Lygeros 1991)
    N=08 : (R. Bayon, N. Lygeros 10/2001)
    N=09 : (R. Bayon, N. Lygeros, J.-S. Sereni 02/2002)
    N=10 : (R. Bayon, N. Lygeros, J.-S. Sereni 06/2002)

    HELPERS : Philippe Alsina, Lionel Baraque, Bruno Carré, Patrice Deloche, Pierre Hyvernat, Rémi Nardini, Matthieu Pérotin, Romain Perron.

    For more information see SSU Project

  • The number of non isomorphic mixed models with factors

    f=1 : 2 (A. Hess, H. Iyer 1999)
    f=2 : 6 (A. Hess, H. Iyer 1999)
    f=3 : 22 (A. Hess, H. Iyer 1999)
    f=4 : 101 (A. Hess, H. Iyer 1999)
    f=5 : 576 (A. Hess, H. Iyer 1999)
    f=6 : 4.162 (R.Bayon, N. Lygeros and J.-S. Sereni 2002)
    f=7 : 38.280 (R.Bayon, N. Lygeros and J.-S. Sereni 2002)
    f=8 : 451.411 (R.Bayon, N. Lygeros and J.-S. Sereni 2002)
    f=9 : 6.847.662 (R.Bayon, N. Lygeros and J.-S. Sereni 2002)

    For more information see Mixed Models Project