Our Mission:
1. To advance European science
to the forefront
of international research
and to stabilize this position.
2. To strengthen cooperation
with international research centers:
-
Harish-Chandra Research Institute,
Allahabad, India
-
Washington and Lee University,
Lexington, Virginia, USA
-
Université Mohammed Premier,
Oujda, Morocco
-
Australian National University,
Canberra, Capital Territory
-
Aichi University of Education,
Nagoya, Japan
-
University of Calgary,
Alberta, Canada
International Conferences:
January 21 - 25, 2019:
Asia-Australia Algebra Conference 2019
Western Sydney University, Parramatta City campus
Sydney, New South Wales, Australia
April 25 - 27, 2019:
Conference on Algebra, Number Theory and Their Applications
Université Mohammed Premier, Faculté des Sciences
Oujda, Region Oriental, Morocco
Daniel C. Mayer's 3 Lectures:
1. Proving the Conjecture of Scholz
2. Differential principal factors
3. Pure Metacyclic Fields
July 1 - 5, 2019:
31st Journées Arithmétiques
Istanbul University, Faculty of Science
JA 2019, Istanbul, Turkey
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Database of Real Quadratic Fundamental Discriminants:
For an explanation see the
Online Encyclopedia of Integer Sequences
(OEIS) A269318.
Here we give the first 2870 terms of this sequence up to 107.
32009,42817,62501,72329,94636,103809,114889,130397,142097,151141,
152949,153949,172252,173944,184137,189237,206776,209765,213913,214028,
214712,219461,220217,250748,252977,255973,259653,265245,275881,282461,
283673,298849,320785,321053,326945,333656,335229,341724,342664,358285,
363397,371965,384369,390876,400369,412277,415432,422573,424236,431761,
449797,459964,460817,468472,471057,471713,476124,476152,486221,486581,
494236,502796,510337,527068,529393,531437,531445,534824,535441,540213,
540365,548549,549133,551384,551692,552392,557657,567473,575729,578581,
586760,593941,595009,597068,600085,602521,621429,621749,626264,626441,
631769,635909,636632,637820,654796,665832,681276,686977,689896,698556,
700313,710652,718705,719105,722893,726933,729293,747496,750376,751657,
775480,775661,781177,782737,782876,783689,784997,785269,790085,801368,
804648,807937,810661,814021,823512,829813,831484,835853,836493,859064,
873969,874684,881689,893029,893689,895449,902333,907629,907709,908241,
916181,935665,939569,940593,942961,943077,944760,945813,946733,948777,
957013,957484,959629,966053,966489,967928,974157,980108,982049,993349,
994008,1001957,1011356,1013737,1018337,1024861,1027436,1030117,1034529,1036669,
1048549,1049305,1049345,1049512,1051449,1054040,1058044,1058156,1063324,1064201,
1067953,1069672,1090877,1093816,1112413,1115337,1122573,1126273,1150732,1162949,
1163516,1165845,1168305,1169789,1172312,1174389,1177036,1179372,1185661,1192780,
1193788,1201813,1202680,1203413,1208557,1211752,1223665,1224201,1227880,1238353,
1240585,1252417,1268041,1269881,1275384,1284277,1303097,1303313,1308952,1313292,
1314845,1315640,1319433,1327101,1333801,1334920,1335736,1340988,1342985,1358556,
1360389,1361545,1364953,1375609,1376905,1381721,1382984,1388253,1398317,1398829,
1399708,1408937,1415965,1419961,1420584,1426597,1429916,1442901,1452185,1463181,
1463729,1469017,1473113,1480280,1482568,1488392,1490653,1493176,1494553,1495877,
1496361,1505573,1512860,1518313,1523656,1525277,1535117,1535357,1536673,1539689,
1551257,1552204,1553516,1556797,1559644,1570213,1571953,1580017,1580709,1595669,
1598189,1600597,1603497,1608524,1610860,1617960,1618493,1621337,1625009,1634709,
1635585,1640053,1642009,1642060,1646817,1650156,1658417,1659109,1664444,1669245,
1675165,1680668,1683849,1686840,1693429,1694649,1695260,1696249,1696945,1697097,
1697701,1698341,1700632,1712488,1712577,1717349,1718753,1721852,1722344,1722893,
1723649,1734184,1741080,1741433,1748537,1750609,1751909,1751980,1753829,1758401,
1762977,1766209,1769353,1771529,1771817,1774184,1777081,1783129,1783641,1787597,
1787945,1789169,1791221,1797321,1801601,1802605,1805621,1807649,1815740,1815765,
1824549,1831097,1831640,1834061,1850997,1855052,1857693,1864345,1864961,1865045,
1868601,1871448,1873869,1874317,1877097,1879621,1880493,1881989,1885153,1886717,
1887436,1889897,1893032,1896833,1912072,1918137,1921661,1936952,1940141,1942385,
1954013,1958629,1963085,1963736,1966441,1970089,1977305,1977452,1979957,1983304,
1987912,1991656,1998764,2008145,2008840,2009293,2014328,2015752,2020712,2021608,
2023845,2030361,2034345,2042149,2043761,2044792,2047768,2047781,2047973,2049869,
2054281,2059253,2071509,2076485,2078060,2087485,2097373,2099101,2109356,2118901,
2119948,2122521,2134129,2142445,2144476,2149372,2154017,2159272,2161601,2163837,
2165945,2166364,2170445,2173864,2175832,2177576,2178049,2181533,2185465,2185789,
2186412,2188941,2196321,2197597,2197669,2208188,2212273,2212669,2219560,2220104,
2222313,2226584,2232473,2234773,2242045,2259761,2289048,2289173,2290748,2294285,
2295205,2297676,2302257,2303112,2307144,2314344,2314789,2328721,2331641,2331985,
2339589,2350121,2351669,2352757,2357573,2360661,2365529,2366049,2368445,2371053,
2374077,2382092,2385996,2391113,2399377,2403337,2408316,2409853,2411101,2417993,
2418456,2427148,2427189,2433221,2443928,2456861,2457749,2457849,2461537,2464557,
2470492,2477413,2496569,2498189,2503804,2508145,2512193,2515388,2518876,2526145,
2527669,2530904,2532085,2538149,2538285,2538417,2539129,2541736,2545181,2548280,
2555249,2557537,2562717,2570685,2571153,2574149,2576005,2582936,2583884,2588381,
2591909,2592044,2595065,2600489,2602129,2606981,2607765,2614717,2624081,2629713,
2630732,2634133,2650045,2657641,2661365,2667452,2672465,2676433,2680409,2683432,
2686865,2689608,2692877,2706029,2706373,2710072,2719756,2720477,2725861,2733965,
2734669,2736309,2744409,2747001,2747021,2751781,2751973,2754616,2756373,2761737,
2765201,2769509,2772481,2776065,2777068,2778616,2778769,2782821,2783477,2785436,
2794873,2798328,2800417,2803001,2805629,2811613,2813221,2816705,2819849,2822344,
2823989,2831912,2836517,2840613,2841596,2843537,2843873,2846776,2848013,2849081,
2849469,2851877,2852733,2853373,2856989,2862856,2876389,2876424,2879841,2882161,
2882204,2883497,2892713,2893317,2904493,2905160,2905745,2906509,2907245,2908005,
2908841,2910601,2915221,2916104,2916121,2918885,2918985,2922737,2926137,2930113,
2931685,2937388,2943273,2947213,2948093,2954584,2954929,2966636,2969029,2969612,
2972168,2986529,2993644,2993992,2996236,2999137,3000853,3005369,3007333,3008389,
3010220,3014365,3018569,3020732,3025117,3030252,3030569,3030997,3034049,3036869,
3038424,3039713,3041509,3045029,3057545,3057709,3058593,3073881,3076732,3081677,
3085349,3088232,3089497,3091133,3091757,3093749,3094529,3097785,3099133,3100956,
3108173,3115481,3122232,3122449,3127145,3132841,3133077,3134365,3138972,3139976,
3143561,3154188,3159777,3163341,3163469,3168113,3174753,3177181,3179548,3180197,
3183505,3186120,3186232,3192053,3193361,3194013,3197209,3197864,3197944,3199445,
3200520,3207937,3209180,3209709,3216173,3218609,3220204,3226345,3231724,3236657,
3243628,3248949,3250136,3253269,3258120,3259597,3264636,3268781,3271237,3282637,
3287877,3291896,3295913,3301681,3303681,3310913,3315373,3321505,3323065,3323976,
3325609,3329617,3331672,3337909,3342785,3342921,3348177,3349277,3351669,3356561,
3362044,3363549,3364684,3366809,3372117,3372549,3386513,3393004,3395228,3398956,
3400232,3409817,3424908,3425621,3426076,3430124,3430645,3433353,3433564,3434568,
3434572,3445345,3449381,3449949,3450601,3451368,3452380,3454844,3461720,3469740,
3469992,3471116,3472653,3476156,3492604,3494789,3496445,3496661,3503605,3505577,
3517689,3518717,3519512,3522145,3525673,3533336,3536205,3538661,3542329,3543193,
3544849,3545420,3552169,3556653,3562872,3568289,3575820,3576588,3581401,3584533,
3586885,3591697,3597960,3606888,3609784,3611704,3631321,3635089,3636221,3639212,
3640137,3644357,3646297,3649605,3651421,3656776,3658421,3660857,3664653,3665157,
3667333,3677677,3678277,3684380,3686561,3687441,3690268,3690785,3692717,3699577,
3702613,3704521,3706953,3708417,3709969,3719897,3721565,3725989,3730913,3735169,
3740169,3743249,3743745,3747880,3763373,3763580,3764741,3764857,3765473,3767469,
3768249,3769228,3770297,3775021,3775069,3776113,3782993,3791996,3794696,3798813,
3799597,3800065,3800409,3800753,3803041,3816785,3821244,3822140,3822185,3832089,
3833021,3836289,3836453,3839449,3856685,3863389,3869884,3869909,3870437,3871304,
3872929,3873116,3875977,3880613,3882909,3884829,3885769,3901740,3903281,3908153,
3916345,3918381,3918837,3928632,3930357,3932653,3934781,3937565,3940765,3944321,
3947341,3948277,3954361,3958712,3965452,3967321,3968392,3973817,3973868,3974945,
3977033,3978097,3982177,3983833,3984601,3988085,3989260,3992693,3995004,3996501,
4000001,4000008,4003621,4006033,4007388,4007976,4015705,4024049,4025909,4026409,
4026680,4029148,4029528,4030376,4031945,4045265,4060065,4064264,4072072,4073233,
4074493,4074828,4074904,4093073,4093285,4102401,4105885,4108205,4115857,4116797,
4120301,4121608,4123569,4127765,4130297,4132609,4133569,4135481,4139273,4139432,
4139468,4149244,4152181,4161369,4164748,4170664,4170764,4171020,4177937,4181497,
4182545,4182637,4183205,4185304,4189624,4195304,4196840,4199773,4199901,4202616,
4211528,4213165,4215560,4220285,4220977,4228364,4233608,4235489,4237768,4241361,
4244957,4249057,4251724,4251817,4252837,4261793,4263105,4265612,4265877,4283276,
4286949,4291244,4292745,4293013,4294732,4295037,4295157,4296533,4297609,4297672,
4297829,4297949,4305957,4311821,4325053,4329429,4330972,4331724,4334716,4335724,
4335752,4335916,4337709,4343064,4343260,4350121,4350776,4357865,4358801,4368012,
4368937,4369768,4370348,4370909,4371637,4372284,4373049,4377149,4380285,4382441,
4384857,4386533,4387868,4390873,4398008,4401085,4405693,4405853,4406501,4409313,
4410613,4417564,4419301,4420949,4423148,4425005,4425229,4429612,4431397,4433068,
4439932,4441560,4447273,4452829,4453069,4477672,4478377,4481797,4486793,4490745,
4492129,4502765,4503945,4508257,4508369,4515341,4522745,4526969,4531029,4531441,
4533032,4534060,4538737,4543781,4546633,4547801,4554476,4562765,4563496,4566001,
4567416,4567809,4568341,4570053,4572797,4577052,4580680,4586797,4592785,4593673,
4598169,4600412,4601244,4617017,4627549,4628117,4644888,4646593,4648280,4662917,
4669309,4672972,4678385,4680701,4684913,4685893,4689397,4695429,4698389,4705737,
4715209,4719464,4721761,4727281,4727609,4732417,4736569,4740013,4740377,4745672,
4745989,4746781,4747721,4755365,4757873,4759969,4760877,4761544,4766309,4768913,
4773212,4776856,4779689,4782664,4783697,4784316,4784809,4785845,4788741,4790641,
4791349,4791829,4796076,4800545,4803545,4815833,4822921,4827065,4832060,4836268,
4836413,4843436,4845432,4848737,4850792,4852009,4858401,4860233,4861432,4861720,
4862445,4866437,4870533,4871221,4882732,4886097,4893260,4895112,4896764,4902349,
4902981,4907417,4912028,4913717,4914721,4920049,4927256,4931101,4937784,4945973,
4947333,4947717,4950924,4959637,4965009,4965469,4967777,4971733,4979857,4994321,
4996597,4997433,5001933,5003085,5006001,5011912,5015805,5016917,5020033,5020581,
5024008,5025389,5032977,5034673,5039692,5041821,5045016,5047816,5048573,5048988,
5049457,5055701,5058169,5062497,5070193,5075977,5077777,5078057,5081557,5087633,
5088829,5090485,5091601,5093581,5103569,5104601,5108353,5109244,5109645,5109889,
5111669,5119637,5121109,5129053,5130220,5137385,5139545,5150273,5154385,5155816,
5155928,5156552,5176785,5178748,5180081,5180341,5183077,5183452,5188205,5188745,
5190369,5195741,5199613,5204865,5212101,5212428,5213213,5217413,5221065,5226941,
5228705,5228844,5235436,5240945,5250748,5250941,5253673,5264069,5268981,5270369,
5271608,5275864,5281301,5284445,5285276,5289016,5291128,5293645,5298109,5299096,
5300265,5302376,5302937,5310460,5313052,5316017,5318905,5319509,5322749,5327080,
5327605,5329749,5334089,5336489,5337341,5338461,5343801,5344017,5348172,5350569,
5353240,5355640,5356097,5357729,5359772,5361461,5362136,5368952,5370061,5372344,
5373761,5373869,5376281,5378028,5378264,5379393,5383565,5386737,5386777,5387145,
5387196,5387593,5395829,5399708,5400712,5401180,5403697,5404165,5409977,5410789,
5415409,5420697,5429948,5432657,5438136,5438413,5443724,5451677,5452568,5461944,
5477673,5478321,5488633,5489333,5489661,5496828,5500365,5502617,5507549,5509397,
5512252,5517649,5520489,5522365,5524268,5530633,5537445,5540540,5542552,5546712,
5547841,5548924,5557388,5557721,5562969,5567797,5568257,5571377,5587141,5588121,
5590309,5590429,5593385,5595377,5597752,5604953,5605229,5609964,5613052,5620973,
5622341,5627573,5649097,5649164,5649421,5650780,5655548,5658968,5659496,5662769,
5665189,5665352,5667713,5670508,5677624,5693576,5693757,5698465,5698505,5698952,
5701693,5702984,5704268,5707693,5708249,5709029,5710793,5714236,5717537,5724373,
5732849,5733113,5734109,5736281,5741809,5748881,5751404,5753996,5754613,5756097,
5764216,5765037,5770533,5771561,5789148,5790221,5791469,5795501,5796508,5800364,
5805192,5807597,5807852,5807944,5808381,5810873,5814872,5815677,5822437,5827564,
5836373,5839921,5848061,5858753,5860741,5863757,5863777,5867160,5867385,5880361,
5884177,5884529,5891701,5893241,5902905,5903276,5909217,5909813,5913197,5919485,
5924449,5931565,5935928,5941196,5955641,5958073,5958181,5963493,5964385,5965112,
5965340,5966364,5967336,5967413,5967473,5968060,5968157,5968489,5973112,5975569,
5976988,5978401,5981469,5982269,5994940,6017749,6024821,6027557,6028408,6031688,
6036188,6037005,6042108,6044232,6047213,6049356,6050921,6052629,6053480,6054060,
6056553,6058309,6061436,6063641,6068989,6070721,6080140,6087413,6088709,6090001,
6090088,6090904,6092941,6093721,6094316,6098360,6100748,6101180,6105693,6105757,
6107897,6115852,6128869,6136028,6138205,6142348,6147676,6150616,6155281,6155788,
6155861,6163144,6178757,6179569,6185656,6187933,6189573,6191961,6194053,6194089,
6196988,6197496,6202313,6204721,6207733,6209308,6218377,6220717,6221449,6224209,
6225133,6229129,6233116,6234501,6239785,6239868,6240860,6241817,6243185,6245036,
6245772,6249873,6256661,6259629,6261116,6262520,6262961,6263720,6266629,6267004,
6267173,6267948,6270961,6272869,6272977,6274549,6274609,6281169,6287948,6290061,
6290549,6298321,6300849,6305496,6305561,6306401,6312921,6314440,6318085,6318733,
6325336,6329905,6335644,6337340,6339317,6342445,6345329,6347685,6348317,6348957,
6349209,6354941,6364409,6366029,6376209,6387272,6389020,6391097,6396593,6397945,
6399401,6401533,6401596,6405317,6408553,6415493,6416953,6418369,6425809,6426069,
6426193,6426869,6428649,6429997,6438541,6442397,6447345,6450437,6451121,6455913,
6457084,6465832,6467036,6468217,6469817,6470077,6470353,6473885,6478012,6478268,
6481753,6487177,6491804,6493645,6500289,6501608,6504697,6508156,6510264,6510712,
6516040,6519373,6523789,6526168,6526680,6533128,6535688,6538220,6540917,6541276,
6548753,6556985,6558305,6560733,6561577,6563020,6563816,6565772,6569484,6578092,
6585896,6587753,6589721,6590060,6590380,6593485,6594905,6595773,6601461,6604793,
6605157,6606236,6607452,6614445,6614689,6615309,6618085,6621421,6625473,6628609,
6630865,6631573,6633169,6634129,6636713,6637537,6642977,6649240,6651377,6652929,
6654041,6654748,6658709,6658973,6663101,6667048,6667645,6678892,6682829,6689613,
6699569,6700321,6703384,6704141,6705921,6709281,6709333,6711528,6719417,6723676,
6729112,6729740,6732412,6735740,6740185,6743093,6743865,6747404,6751273,6752157,
6753937,6758101,6771061,6772541,6773557,6773997,6775224,6775529,6778181,6791813,
6792365,6794348,6794641,6796581,6803481,6805237,6806152,6808609,6813061,6813109,
6824285,6825721,6826205,6838840,6845084,6845336,6850092,6856405,6857165,6858568,
6859661,6860024,6860145,6860417,6864924,6865564,6871197,6876329,6882737,6886913,
6888889,6889180,6895612,6898245,6904265,6910077,6911265,6918245,6922504,6926485,
6927452,6931976,6935020,6946573,6946689,6950693,6953513,6963629,6967628,6972169,
6974141,6974609,6980856,6984521,6999848,7002680,7004924,7010133,7017169,7017736,
7017916,7019717,7023993,7026477,7028920,7032201,7038616,7038617,7039580,7041161,
7047185,7047416,7047649,7049129,7052865,7055277,7055413,7057581,7057592,7061009,
7064133,7066284,7066561,7075740,7077020,7080172,7080889,7081624,7086217,7088593,
7093661,7100889,7101041,7102277,7102389,7107513,7107976,7109452,7116424,7119836,
7120668,7123493,7127285,7128233,7133757,7143861,7145041,7145857,7147420,7147533,
7150249,7153097,7154693,7160561,7160952,7164681,7167928,7170301,7172184,7176477,
7176945,7178469,7183797,7189809,7208173,7209221,7213289,7216009,7219073,7219372,
7219469,7222793,7228885,7230221,7231685,7234141,7235773,7239405,7241516,7242929,
7245561,7247080,7250809,7261244,7263365,7269421,7273797,7274173,7277084,7278357,
7279717,7285809,7288601,7290040,7291933,7299209,7300952,7300985,7304521,7304941,
7310585,7312040,7313928,7321969,7327265,7331224,7331309,7338248,7339397,7342237,
7343393,7348805,7352620,7358937,7359857,7364145,7365785,7367161,7377420,7378853,
7381932,7388524,7391212,7393416,7397564,7400657,7401229,7403861,7406249,7406277,
7415137,7415841,7415852,7419813,7421997,7425733,7428617,7431980,7432345,7442897,
7443833,7445317,7447697,7452897,7452984,7456945,7459773,7465196,7466572,7468808,
7470769,7472029,7475905,7479132,7480360,7481093,7481593,7482353,7486445,7488337,
7491929,7499497,7499557,7502501,7503493,7511605,7514437,7514473,7517081,7517621,
7519117,7519997,7521609,7526561,7526744,7528205,7528828,7531592,7531593,7538045,
7539061,7539141,7541245,7546933,7550005,7558457,7561077,7566072,7567141,7571669,
7573868,7577436,7577893,7579553,7582988,7584508,7589001,7589509,7590073,7591013,
7597740,7598609,7601081,7601305,7601461,7611009,7612424,7612945,7614037,7623320,
7627009,7629644,7630321,7630645,7634065,7636760,7638297,7639609,7641292,7643993,
7646945,7647733,7648012,7654305,7655989,7657037,7662401,7663549,7664845,7665064,
7666737,7667781,7670697,7672472,7676236,7676393,7676853,7683308,7684005,7684945,
7687373,7691153,7692469,7701509,7702477,7702901,7704653,7712184,7713961,7714680,
7715057,7715580,7715929,7718981,7721977,7724481,7726216,7728713,7729512,7731096,
7732121,7736749,7738401,7738629,7739404,7745677,7758589,7759533,7761185,7762296,
7763361,7766524,7770509,7773512,7773944,7774229,7785149,7785965,7793153,7795564,
7795617,7798057,7798333,7804828,7816376,7818905,7822361,7824697,7824889,7844520,
7849853,7857048,7861057,7868281,7873885,7877697,7879505,7880801,7881144,7881701,
7883233,7886812,7887369,7888805,7890508,7891465,7892349,7892648,7893493,7893564,
7893609,7896221,7896397,7903769,7911697,7913868,7917304,7920133,7923361,7928565,
7929244,7931289,7936316,7937932,7942985,7943761,7951921,7956968,7957661,7957724,
7960193,7962721,7967489,7970953,7975068,7982392,7984333,7984857,7998493,7999624,
7999901,8003741,8004001,8005429,8011685,8012728,8018616,8025537,8027288,8037645,
8040029,8043845,8050985,8053217,8053469,8055505,8069356,8070637,8072293,8079101,
8084540,8085909,8088652,8089365,8091453,8098849,8101277,8102053,8105313,8105912,
8107129,8108589,8110109,8111384,8115416,8118709,8118796,8119933,8124796,8124961,
8127208,8131289,8132381,8140953,8141473,8143617,8151661,8153692,8157937,8160545,
8168968,8169593,8172137,8173849,8176856,8178808,8180669,8182129,8183381,8187689,
8189621,8189644,8193533,8193724,8197753,8208632,8208993,8211509,8213089,8213189,
8214745,8215689,8216213,8231269,8232753,8234833,8235820,8235965,8241976,8243113,
8243464,8248953,8251521,8257368,8260061,8261305,8263020,8264609,8265560,8269116,
8272712,8273129,8274092,8279149,8298421,8300053,8308312,8310701,8311756,8312061,
8314201,8317112,8320301,8320764,8321269,8321505,8321932,8326841,8327597,8328104,
8331081,8331353,8335032,8336001,8341681,8343689,8343941,8344617,8347989,8348793,
8352060,8355533,8355941,8356760,8358745,8360609,8360885,8363793,8364253,8364568,
8365336,8366408,8366793,8369448,8369468,8374481,8375228,8377865,8382265,8382997,
8388581,8391937,8392801,8393149,8396833,8397932,8404536,8405605,8415804,8421976,
8423077,8424569,8424749,8427820,8429397,8434268,8438333,8446289,8448184,8448673,
8449265,8450524,8453985,8462136,8463752,8467009,8470577,8471069,8472252,8481576,
8482865,8483869,8484721,8490277,8491713,8492408,8496937,8501541,8505980,8506013,
8508076,8511773,8520045,8520568,8523385,8535116,8536409,8536793,8538108,8542369,
8543057,8553797,8554081,8554952,8558680,8558984,8559737,8567333,8568161,8578617,
8582249,8583061,8592261,8593689,8596124,8596597,8603401,8604033,8609833,8614184,
8614245,8616297,8616381,8619880,8621821,8623704,8626101,8627820,8632716,8633045,
8637717,8637753,8643669,8648297,8648617,8649717,8652165,8654009,8664737,8664989,
8667244,8668165,8673069,8674397,8676077,8678649,8679416,8682856,8683261,8696989,
8698568,8698616,8699624,8700765,8701489,8706329,8708613,8709976,8710216,8711453,
8711501,8714168,8723237,8732085,8735529,8737109,8737913,8738077,8738936,8739521,
8739708,8741384,8746008,8747068,8747997,8748764,8751961,8754856,8756024,8757053,
8760093,8762408,8771896,8776216,8776536,8778505,8778845,8786789,8787052,8789577,
8791813,8798117,8798529,8801957,8805372,8807217,8808413,8810201,8814097,8816389,
8817153,8818505,8825720,8826652,8826809,8834613,8834645,8835581,8836220,8836460,
8837756,8846056,8847169,8849964,8854465,8857288,8857581,8859805,8861245,8861753,
8863273,8865617,8865884,8873417,8874185,8875772,8876812,8878981,8881772,8881969,
8882732,8890549,8894929,8895349,8897192,8899661,8902433,8903677,8907240,8909304,
8909633,8910321,8912901,8914888,8921757,8922101,8936376,8939224,8942908,8943708,
8946940,8949029,8949688,8950297,8951297,8951513,8952341,8952956,8953045,8957485,
8958081,8960568,8963117,8965093,8966109,8969653,8970409,8970889,8974001,8981848,
8986917,8988673,8993409,9006397,9010236,9010828,9013853,9017580,9025388,9025768,
9036057,9036461,9037068,9048757,9051665,9054152,9054177,9055549,9056101,9057941,
9058892,9061372,9062184,9064513,9066193,9072537,9073144,9073352,9074152,9078505,
9087116,9087629,9089017,9089817,9092273,9093809,9094040,9094989,9095180,9095377,
9105261,9107176,9116153,9117569,9118841,9120921,9125373,9125617,9129480,9130485,
9130973,9131165,9131429,9133145,9137737,9137749,9139820,9149937,9151149,9152105,
9153129,9155089,9160140,9162577,9162653,9166765,9167801,9173897,9174581,9182229,
9185153,9186929,9186933,9188033,9195769,9199633,9202444,9205885,9210805,9212428,
9215420,9234221,9235896,9242717,9247009,9248889,9250177,9250861,9251089,9253868,
9256764,9259429,9264109,9265288,9271353,9272021,9272165,9273013,9276601,9277033,
9289484,9290809,9293736,9294764,9298273,9299389,9303505,9303861,9307085,9310332,
9311708,9314140,9314889,9320684,9320693,9320812,9321765,9328597,9334229,9340952,
9343336,9345516,9347505,9351320,9351697,9354441,9355004,9358901,9363480,9368121,
9368821,9370565,9377141,9377149,9379849,9380744,9383309,9390293,9392357,9396893,
9405985,9409405,9409688,9414897,9417532,9419261,9419569,9419704,9420317,9425017,
9430716,9433849,9438413,9438881,9441097,9441265,9443293,9445693,9447661,9448265,
9452221,9455624,9459672,9459676,9460648,9467897,9470364,9480773,9483784,9485416,
9487996,9491253,9491781,9497017,9500453,9504777,9505672,9507692,9509701,9511580,
9516005,9519389,9519448,9527992,9531233,9531752,9532297,9533357,9540781,9541445,
9541948,9544252,9551512,9557128,9560093,9564161,9564773,9565441,9569365,9574348,
9576508,9577541,9579692,9580645,9583736,9586357,9586481,9590757,9591528,9593357,
9593853,9595409,9597473,9598477,9600569,9601429,9603733,9609464,9609832,9610509,
9612253,9615813,9620201,9622408,9623741,9627720,9632957,9633965,9644761,9645393,
9651932,9652088,9653341,9655384,9655768,9660641,9661713,9663833,9667441,9668044,
9669629,9670821,9674841,9675260,9677269,9682089,9682121,9688501,9690321,9691357,
9694801,9697301,9698952,9703644,9703877,9712812,9714921,9717976,9720152,9720337,
9730637,9731185,9731276,9746609,9747865,9749393,9751629,9758461,9764309,9770989,
9771224,9775301,9775589,9776801,9786641,9789101,9792245,9794141,9794897,9795041,
9801773,9809180,9809801,9812669,9813457,9816401,9818149,9818273,9821960,9827617,
9830236,9834557,9844696,9848433,9848805,9849557,9852505,9857805,9861249,9863537,
9866985,9873212,9873841,9874401,9880620,9884677,9885637,9886313,9886705,9888109,
9893941,9901561,9905473,9907837,9908929,9915701,9922641,9923685,9924456,9924821,
9927877,9937093,9938697,9941989,9942961,9944121,9944369,9945905,9947969,9952745,
9956945,9957761,9958876,9964821,9965292,9967837,9968065,9970793,9971821,9972617,
9972733,9980204,9984085,9984296,9985009,9985517,9987061,9990597,9991432,9998337.
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