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Powered to perfect (Posted on 2021-02-07) Difficulty: 4 of 5
A positive integer m is perfect if the sum of all its positive divisors, 1 and m inclusive, is equal to 2m.

Determine the positive integers n such that nn+1 is a perfect number.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.6667 (3 votes)

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making it more probable | Comment 2 of 7 |
The below lists up to the first 15 digits on n^n+1 as well as the number of digits in the whole number. This is for comparison to the Wikipedia List of perfect numbers (https://en.wikipedia.org/wiki/List_of_perfect_numbers) in approximately the same format.

Only 28 appears on both lists. However, my list stops at 1000^1000+1.

(a second list, using a different algorithm, follows the first, going up to 10,000^10,000_

n, n^n+1 first digits,  number of digits

[ 2.0, 5.0, 1]
[ 3.0, 28.0, 2]
[ 4.0, 257.0, 3]
[ 5.0, 3126.0, 4]
[ 6.0, 46657.0, 5]
[ 7.0, 823544.0, 6]
[ 8.0, 16777217.0, 8]
[ 9.0, 387420490.0, 9]
[ 10.0, 10000000001.0, 11]
[ 11.0, 285311670612.0, 12]
[ 12.0, 8916100448257.0, 13]
[ 13.0, 30287510659225, 15]
[ 14.0, 11112006825558, 17]
[ 15.0, 43789389038085, 18]
[ 16.0, 18446744073709, 20]
[ 17.0, 82724026188633, 21]
[ 18.0, 39346408075296, 23]
[ 19.0, 19784196556603, 25]
[ 20.0, 10485760000000, 27]
[ 21.0, 58425870183859, 28]
[ 22.0, 34142787736421, 30]
[ 23.0, 20880467999847, 32]
[ 24.0, 13337357768502, 34]
[ 25.0, 88817841970012, 35]
[ 26.0, 61561195802071, 37]
[ 27.0, 44342648824303, 39]
[ 28.0, 33145523113253, 41]
[ 29.0, 25676861531612, 43]
[ 30.0, 20589113209464, 45]
[ 31.0, 17069174130723, 47]
[ 32.0, 14615016373309, 49]
[ 33.0, 12911004008776, 51]
[ 34.0, 11756638905368, 53]
[ 35.0, 11025074993541, 55]
[ 36.0, 10638735892371, 57]
[ 37.0, 10555134955777, 59]
[ 38.0, 10759118019799, 61]
[ 39.0, 11259514746207, 63]
[ 40.0, 12089258196146, 65]
[ 41.0, 13308776306327, 67]
[ 42.0, 15013093754529, 69]
[ 43.0, 17343773367030, 71]
[ 44.0, 20507738235606, 73]
[ 45.0, 24806364445134, 75]
[ 46.0, 30680346300794, 77]
[ 47.0, 38779242634644, 79]
[ 48.0, 50070207826345, 81]
[ 49.0, 66009724686219, 83]
[ 50.0, 88817841970012, 85]
[ 51.0, 12192113050946, 88]
[ 52.0, 17067655527413, 90]
[ 53.0, 24356848165022, 92]
[ 54.0, 35421180450106, 94]
[ 55.0, 52474453246875, 96]
[ 56.0, 79164324866862, 98]
[ 57.0, 12158129736671, 101]
[ 58.0, 19003063809415, 103]
[ 59.0, 30218206653543, 105]
[ 60.0, 48873677980689, 107]
[ 61.0, 80374805625459, 109]
[ 62.0, 13436456451522, 112]
[ 63.0, 22827303634696, 114]
[ 64.0, 39402006196394, 116]
[ 65.0, 69082521647609, 118]
[ 66.0, 12299848035352, 121]
[ 67.0, 22233702024236, 123]
[ 68.0, 40794917954274, 125]
[ 69.0, 75960403121632, 127]
[ 70.0, 14350360160986, 130]
[ 71.0, 27500637348346, 132]
[ 72.0, 53449019547361, 134]
[ 73.0, 10533405146807, 137]
[ 74.0, 21044919075854, 139]
[ 75.0, 42618165776125, 141]
[ 76.0, 87464740776733, 143]
[ 77.0, 18188037387806, 146]
[ 78.0, 38315898123134, 148]
[ 79.0, 81759873707105, 150]
[ 80.0, 17668470647783, 153]
[ 81.0, 38662196978715, 155]
[ 82.0, 85651681910278, 157]
[ 83.0, 19207978777850, 160]
[ 84.0, 43597343682732, 162]
[ 85.0, 10014025332845, 165]
[ 86.0, 23273773687010, 167]
[ 87.0, 54723640075158, 169]
[ 88.0, 13015928349429, 172]
[ 89.0, 31311984360626, 174]
[ 90.0, 76177348045866, 176]
[ 91.0, 18739875497044, 179]
[ 92.0, 46610108703636, 181]
[ 93.0, 11719638492654, 184]
[ 94.0, 29786415160527, 186]
[ 95.0, 76514281153818, 188]
[ 96.0, 19862704051982, 191]
[ 97.0, 52102459397183, 193]
[ 98.0, 13808783412614, 196]
[ 99.0, 36972963764972, 198]
[ 100.0, 10000000000000, 200]
[ 101.0, 27318619677157, 203]
[ 102.0, 75373298214297, 205]
[ 103.0, 21000718068545, 208]
[ 104.0, 59083645955724, 210]
[ 105.0, 16783263083479, 213]
[ 106.0, 48130649029357, 215]
[ 107.0, 13933628024324, 218]
[ 108.0, 40716045647697, 220]
[ 109.0, 12008486537529, 223]
[ 110.0, 35743359351975, 225]
[ 111.0, 10736201288847, 228]
[ 112.0, 32540074211370, 230]
[ 113.0, 99509401373215, 232]
[ 114.0, 30701037516868, 235]
[ 115.0, 95554609203025, 237]
[ 116.0, 30000379625200, 240]
[ 117.0, 95004860435097, 242]
[ 118.0, 30344281745613, 245]
[ 119.0, 97743616924752, 247]
[ 120.0, 31750423737803, 250]
[ 121.0, 10399915443693, 253]
[ 122.0, 34347832971354, 255]
[ 123.0, 11437436793461, 258]
[ 124.0, 38396263207766, 260]
[ 125.0, 12994262207056, 263]
[ 126.0, 44329076602207, 265]
[ 127.0, 15243074119957, 268]
[ 128.0, 52829453113566, 270]
[ 129.0, 18453239934385, 273]
[ 130.0, 64958471898792, 275]
[ 131.0, 23043037728555, 278]
[ 132.0, 82368075538293, 280]
[ 133.0, 29666632286057, 283]
[ 134.0, 10765717535887, 286]
[ 135.0, 39360331440417, 288]
[ 136.0, 14497447287989, 291]
[ 137.0, 53792001073667, 293]
[ 138.0, 20105455807543, 296]
[ 139.0, 75693264399008, 298]
[ 140.0, 28702848252332, 301]
[ 141.0, 10962128393133, 304]
[ 142.0, 42164300748291, 306]
[ 143.0, 16332525972973, 309]
[ 144.0, 63708717381247, 311]
[ 145.0, 25024207011349, 314]
[ 146.0, 98973047865507, 316]
[ 147.0, 39413790878674, 319]
[ 148.0, 15802793986599, 322]
[ 149.0, 63790204353942, 324]
[ 150.0, 25923214794879, 327]
[ 151.0, 10605204349607, 330]
[ 152.0, 43674241135072, 332]
[ 153.0, 18104599210571, 335]
[ 154.0, 75542440087865, 337]
[ 155.0, 31725846335793, 340]
[ 156.0, 13410264483540, 343]
[ 157.0, 57048657424979, 345]
[ 158.0, 24424165763524, 348]
[ 159.0, 10523077453102, 351]
[ 160.0, 45624406176221, 353]
[ 161.0, 19905176879683, 356]
[ 162.0, 87384087578448, 358]
[ 163.0, 38599307914730, 361]
[ 164.0, 17155014118803, 364]
[ 165.0, 76709790259188, 366]
[ 166.0, 34509813690037, 369]
[ 167.0, 15618908534241, 372]
[ 168.0, 71114691428439, 374]
[ 169.0, 32572649024001, 377]
[ 170.0, 15007786205529, 380]
[ 171.0, 69556044564380, 382]
[ 172.0, 32425961901630, 385]
[ 173.0, 15204629478199, 388]
[ 174.0, 71708262756214, 390]
[ 175.0, 34014063652936, 393]
[ 176.0, 16226674903478, 396]
[ 177.0, 77851708175854, 398]
[ 178.0, 37563012170865, 401]
[ 179.0, 18226049498508, 404]
[ 180.0, 88930537781955, 406]
[ 181.0, 43633701002008, 409]
[ 182.0, 21527451193549, 412]
[ 183.0, 10679463128902, 415]
[ 184.0, 53269599762445, 417]
[ 185.0, 26715896639084, 420]
[ 186.0, 13471241583614, 423]
[ 187.0, 68293665383376, 425]
[ 188.0, 34807726798252, 428]
[ 189.0, 17835323405271, 431]
[ 190.0, 91872213705547, 433]
[ 191.0, 47574380782495, 436]
[ 192.0, 24764861932931, 439]
[ 193.0, 12958676208002, 442]
[ 194.0, 68160945549097, 444]
[ 195.0, 36037048619292, 447]
[ 196.0, 19150935159888, 450]
[ 197.0, 10229315033442, 453]
[ 198.0, 54917109653787, 455]
[ 199.0, 29632084641717, 458]
[ 200.0, 16069380442589, 461]
[ 201.0, 87580524452147, 463]
[ 202.0, 47970763222787, 466]
[ 203.0, 26405579097166, 469]
[ 204.0, 14606768789817, 472]
[ 205.0, 81197286586275, 474]
[ 206.0, 45357321074985, 477]
[ 207.0, 25460182336218, 480]
[ 208.0, 14360635934016, 483]
[ 209.0, 81390515133792, 485]
[ 210.0, 46350230061129, 488]
[ 211.0, 26521499060013, 491]
[ 212.0, 15247636041968, 494]
[ 213.0, 88075584187706, 496]
[ 214.0, 51114897791904, 499]
[ 215.0, 29803610694742, 502]
[ 216.0, 17458633517997, 505]
[ 217.0, 10274536637851, 508]
[ 218.0, 60745709064698, 510]
[ 219.0, 36079553139769, 513]
[ 220.0, 21527310795459, 516]
[ 221.0, 12903053096367, 519]
[ 222.0, 77689142522643, 521]
[ 223.0, 46987729479256, 524]
[ 224.0, 28546712872383, 527]
[ 225.0, 17420739036775, 530]
[ 226.0, 10678426120716, 533]
[ 227.0, 65746037458577, 535]
[ 228.0, 40657916171630, 538]
[ 229.0, 25253725518638, 541]
[ 230.0, 15754415096288, 544]
[ 231.0, 98711409918921, 546]
[ 232.0, 62117289177163, 549]
[ 233.0, 39258129118496, 552]
[ 234.0, 24917853834385, 555]
[ 235.0, 15883552171529, 558]
[ 236.0, 10167933587775, 561]
[ 237.0, 65366917337350, 563]
[ 238.0, 42200323427409, 566]
[ 239.0, 27358880759570, 569]
[ 240.0, 17811398107286, 572]
[ 241.0, 11644135767226, 575]
[ 242.0, 76439628423752, 577]
[ 243.0, 50387694130894, 580]
[ 244.0, 33351673199434, 583]
[ 245.0, 22166170492261, 586]
[ 246.0, 14792321844458, 589]
[ 247.0, 99116841720033, 591]
[ 248.0, 66683263302893, 594]
[ 249.0, 45044049477268, 597]
[ 250.0, 30549363634996, 600]
[ 251.0, 20801952087336, 603]
[ 252.0, 14221201073342, 606]
[ 253.0, 97609448161869, 608]
[ 254.0, 67261108657220, 611]
[ 255.0, 46531388344983, 614]
[ 256.0, 32317006071311, 617]
[ 257.0, 22532672065650, 620]
[ 258.0, 15771904492305, 623]
[ 259.0, 11082529526686, 626]
[ 260.0, 78175464862820, 628]
[ 261.0, 55356983330827, 631]
[ 262.0, 39349419131671, 634]
[ 263.0, 28077720905598, 637]
[ 264.0, 20111140201788, 640]
[ 265.0, 14459610459136, 643]
[ 266.0, 10435550014516, 646]
[ 267.0, 75597386971047, 648]
[ 268.0, 54969881369446, 651]
[ 269.0, 40120221370060, 654]
[ 270.0, 29391132654539, 657]
[ 271.0, 21611147473880, 660]
[ 272.0, 15949309925677, 663]
[ 273.0, 11814154393007, 666]
[ 274.0, 87832291371231, 668]
[ 275.0, 65537640734847, 671]
[ 276.0, 49080236865166, 674]
[ 277.0, 36888927671366, 677]
[ 278.0, 27826159182272, 680]
[ 279.0, 21065545670296, 683]
[ 280.0, 16004745619204, 686]
[ 281.0, 12203260814131, 689]
[ 282.0, 93378855365038, 691]
[ 283.0, 71706950472472, 694]
[ 284.0, 55259706427912, 697]
[ 285.0, 42735137183994, 700]
[ 286.0, 33165417970326, 703]
[ 287.0, 25828807923811, 706]
[ 288.0, 20185358853274, 709]
[ 289.0, 15829841144017, 712]
[ 290.0, 12457169985547, 715]
[ 291.0, 98369348461938, 717]
[ 292.0, 77945782793782, 720]
[ 293.0, 61974461772549, 723]
[ 294.0, 49444175717254, 726]
[ 295.0, 39581724672794, 729]
[ 296.0, 31794095430782, 732]
[ 297.0, 25625092821803, 735]
[ 298.0, 20722716934820, 738]
[ 299.0, 16814552323790, 741]
[ 300.0, 13689147905858, 744]
[ 301.0, 11181888921282, 747]
[ 302.0, 91642467263641, 749]
[ 303.0, 75355756864368, 752]
[ 304.0, 62168360890518, 755]
[ 305.0, 51457774655704, 758]
[ 306.0, 42732323092070, 761]
[ 307.0, 35602563646477, 764]
[ 308.0, 29759160942053, 767]
[ 309.0, 24955722184559, 770]
[ 310.0, 20995445224777, 773]
[ 311.0, 17720704652885, 776]
[ 312.0, 15004907888979, 779]
[ 313.0, 12746109703002, 782]
[ 314.0, 10861992410083, 785]
[ 315.0, 92859094355394, 787]
[ 316.0, 79637589728706, 790]
[ 317.0, 68515072722521, 793]
[ 318.0, 59132216056016, 796]
[ 319.0, 51195041011523, 799]
[ 320.0, 44462416477094, 802]
[ 321.0, 38736056179663, 805]
[ 322.0, 33852495268226, 808]
[ 323.0, 29676638943260, 811]
[ 324.0, 26096562627238, 814]
[ 325.0, 23019310877234, 817]
[ 326.0, 20367495177275, 820]
[ 327.0, 18076532232903, 823]
[ 328.0, 16092396975515, 826]
[ 329.0, 14369790136888, 829]
[ 330.0, 12870640495445, 832]
[ 331.0, 11562877902544, 835]
[ 332.0, 10419425883473, 838]
[ 333.0, 94173726847307, 840]
[ 334.0, 85372876607969, 843]
[ 335.0, 77626562930607, 846]
[ 336.0, 70794122497377, 849]
[ 337.0, 64755489946700, 852]
[ 338.0, 59407967438760, 855]
[ 339.0, 54663532165135, 858]
[ 340.0, 50446587616140, 861]
[ 341.0, 46692081665379, 864]
[ 342.0, 43343928491938, 867]
[ 343.0, 40353682685367, 870]
[ 344.0, 37679423083188, 873]
[ 345.0, 35284811387020, 876]
[ 346.0, 33138296720551, 879]
[ 347.0, 31212442294197, 882]
[ 348.0, 29483354438603, 885]
[ 349.0, 27930197632416, 888]
[ 350.0, 26534781915683, 891]
[ 351.0, 25281211359443, 894]
[ 352.0, 24155584143875, 897]
[ 353.0, 23145736354091, 900]
[ 354.0, 22241022893133, 903]
[ 355.0, 21432129983609, 906]
[ 356.0, 20710914621758, 909]
[ 357.0, 20070267092159, 912]
[ 358.0, 19503993274009, 915]
[ 359.0, 19006713991992, 918]
[ 360.0, 18573779103967, 921]
[ 361.0, 18201194388293, 924]
[ 362.0, 17885559607617, 927]
[ 363.0, 17624016393260, 930]
[ 364.0, 17414204823116, 933]
[ 365.0, 17254227763212, 936]
[ 366.0, 17142622214509, 939]
[ 367.0, 17078337057106, 942]
[ 368.0, 17060716717903, 945]
[ 369.0, 17089490408745, 948]
[ 370.0, 17164766693205, 951]
[ 371.0, 17287033244424, 954]
[ 372.0, 17457161756512, 957]
[ 373.0, 17676418070253, 960]
[ 374.0, 17946477672906, 963]
[ 375.0, 18269446833956, 966]
[ 376.0, 18647889746351, 969]
[ 377.0, 19084862158675, 972]
[ 378.0, 19583952110672, 975]
[ 379.0, 20149328525703, 978]
[ 380.0, 20785798572725, 981]
[ 381.0, 21498874891151, 984]
[ 382.0, 22294853979315, 987]
[ 383.0, 23180907286633, 990]
[ 384.0, 24165186827364, 993]
[ 385.0, 25256947457712, 996]
[ 386.0, 26466688336951, 999]
[ 387.0, 27806316537868, 1002]
[ 388.0, 29289336295025, 1005]
[ 389.0, 30931067996346, 1008]
[ 390.0, 32748901752619, 1011]
[ 391.0, 34762591242772, 1014]
[ 392.0, 36994594556534, 1017]
[ 393.0, 39470469972340, 1020]
[ 394.0, 42219336055404, 1023]
[ 395.0, 45274407185295, 1026]
[ 396.0, 48673617680348, 1029]
[ 397.0, 52460350145900, 1032]
[ 398.0, 56684286617384, 1035]
[ 399.0, 61402404598249, 1038]
[ 400.0, 66680144328798, 1041]
[ 401.0, 72592778714315, 1044]
[ 402.0, 79227023471298, 1047]
[ 403.0, 86682932441387, 1050]
[ 404.0, 95076131945757, 1053]
[ 405.0, 10454045884164, 1057]
[ 406.0, 11523108000644, 1060]
[ 407.0, 12732818681618, 1063]
[ 408.0, 14104137742280, 1066]
[ 409.0, 15661486303132, 1069]
[ 410.0, 17433366287477, 1072]
[ 411.0, 19453098734452, 1075]
[ 412.0, 21759705119703, 1078]
[ 413.0, 24398961070901, 1081]
[ 414.0, 27424658230721, 1084]
[ 415.0, 30900117831087, 1087]
[ 416.0, 34900009142246, 1090]
[ 417.0, 39512537776126, 1093]
[ 418.0, 44842083389152, 1096]
[ 419.0, 51012384312742, 1099]
[ 420.0, 58170388875949, 1102]
[ 421.0, 66490920722382, 1105]
[ 422.0, 76182339579488, 1108]
[ 423.0, 87493421368660, 1111]
[ 424.0, 10072173433630, 1115]
[ 425.0, 11622385367145, 1118]
[ 426.0, 13442783918182, 1121]
[ 427.0, 15584850323689, 1124]
[ 428.0, 18110612469047, 1127]
[ 429.0, 21094942563866, 1130]
[ 430.0, 24628383026423, 1133]
[ 431.0, 28820627962827, 1136]
[ 432.0, 33804819707701, 1139]
[ 433.0, 39742860379197, 1142]
[ 434.0, 46831989576694, 1145]
[ 435.0, 55312944140862, 1148]
[ 436.0, 65480098057521, 1151]
[ 437.0, 77694084944257, 1154]
[ 438.0, 92397538322433, 1157]
[ 439.0, 11013475405331, 1161]
[ 440.0, 13157629524227, 1164]
[ 441.0, 15754983595691, 1167]
[ 442.0, 18907889357632, 1170]
[ 443.0, 22743155294858, 1173]
[ 444.0, 27418186796302, 1176]
[ 445.0, 33128737561450, 1179]
[ 446.0, 40118712364486, 1182]
[ 447.0, 48692586000151, 1185]
[ 448.0, 59231164513896, 1188]
[ 449.0, 72211623724283, 1191]
[ 450.0, 88233031090307, 1194]
[ 451.0, 10804890922675, 1198]
[ 452.0, 13260885791617, 1201]
[ 453.0, 16311184937443, 1204]
[ 454.0, 20107459245171, 1207]
[ 455.0, 24841938311260, 1210]
[ 456.0, 30758719738023, 1213]
[ 457.0, 38168354035272, 1216]
[ 458.0, 47466687563080, 1219]
[ 459.0, 59159250282606, 1222]
[ 460.0, 73892876573467, 1225]
[ 461.0, 92496777933002, 1228]
[ 462.0, 11603598866261, 1232]
[ 463.0, 14588103681976, 1235]
[ 464.0, 18379892944429, 1238]
[ 465.0, 23207218638759, 1241]
[ 466.0, 29365484966150, 1244]
[ 467.0, 37237732204418, 1247]
[ 468.0, 47321580220029, 1250]
[ 469.0, 60264732527261, 1253]
[ 470.0, 76911845041251, 1256]
[ 471.0, 98366508782052, 1259]
[ 472.0, 12607336808590, 1263]
[ 473.0, 16192711153772, 1266]
[ 474.0, 20841739027283, 1269]
[ 475.0, 26882185388793, 1272]
[ 476.0, 34746374399342, 1275]
[ 477.0, 45005625512073, 1278]
[ 478.0, 58416371913555, 1281]
[ 479.0, 75982035812778, 1284]
[ 480.0, 99036193633625, 1287]
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[ 945.0, 60681881948884, 2812]
[ 946.0, 15596064984174, 2816]
[ 947.0, 40126392423420, 2819]
[ 948.0, 10334840929286, 2823]
[ 949.0, 26646219033645, 2826]
[ 950.0, 68774117201471, 2829]
[ 951.0, 17769352692561, 2833]
[ 952.0, 45959454148903, 2836]
[ 953.0, 11899653301352, 2840]
[ 954.0, 30842492493493, 2843]
[ 955.0, 80023927526183, 2846]
[ 956.0, 20784760088296, 2850]
[ 957.0, 54041133844642, 2853]
[ 958.0, 14065581686167, 2857]
[ 959.0, 36647493515322, 2860]
[ 960.0, 95583673620218, 2863]
[ 961.0, 24956032898559, 2867]
[ 962.0, 65225782865401, 2870]
[ 963.0, 17065322537299, 2874]
[ 964.0, 44695179144391, 2877]
[ 965.0, 11718104772762, 2881]
[ 966.0, 30754177554402, 2884]
[ 967.0, 80797967904484, 2887]
[ 968.0, 21249360991468, 2891]
[ 969.0, 55942254181199, 2894]
[ 970.0, 14742876865233, 2898]
[ 971.0, 38893071380095, 2901]
[ 972.0, 10270923826936, 2905]
[ 973.0, 27151484600042, 2908]
[ 974.0, 71849541284139, 2911]
[ 975.0, 19032695789242, 2915]
[ 976.0, 50468691238462, 2918]
[ 977.0, 13396419947784, 2922]
[ 978.0, 35595900347756, 2925]
[ 979.0, 94679351647423, 2928]
[ 980.0, 25208916436266, 2932]
[ 981.0, 67188700232311, 2935]
[ 982.0, 17925901544192, 2939]
[ 983.0, 47874916442379, 2942]
[ 984.0, 12799024088677, 2946]
[ 985.0, 34252087133464, 2949]
[ 986.0, 91756773127556, 2952]
[ 987.0, 24605357811401, 2956]
[ 988.0, 66048240486573, 2959]
[ 989.0, 17747304043153, 2963]
[ 990.0, 47735629225333, 2966]
[ 991.0, 12852617854662, 2970]
[ 992.0, 34640071274985, 2973]
[ 993.0, 93455261258151, 2976]
[ 994.0, 25238648249783, 2980]
[ 995.0, 68228424363855, 2983]
[ 996.0, 18462948998246, 2987]
[ 997.0, 50011840417541, 2990]
[ 998.0, 13560640564363, 2994]
[ 999.0, 36806348825922, 2997]
[ 1000.0, 10000000000000, 3000]

clc
digits 10000
for n=vpa(2):vpa(1000)
%    disp(n)
    m=n^n+vpa(1);
    if strlength(string(m))>15
       mc=extractBefore(string(m),15);
    else
        mc=m;
    end
    disp ([n mc ceil(log(m)/log(10))])
end





Actually, since we only need the first few digits as well as the number of digits, we can proceed farther than the limitations of MATLAB's variable precision arithmetic by using logarithms:

clc

for n = 1001:10000
    lm=n*log(n)/log(10);
    mant=lm-floor(lm);
    disp ([n 10^mant ceil(lm)])
end

None of the below matched subsequent perfect numbers:

 1001           27196408561658     3004
 1002          740383913715633     3007
 1003          201760348543707     3011
 1004          550361011589391     3014
 1005            1502768438357     3018

...

the list continues with more than will fit here.

  Posted by Charlie on 2021-02-07 12:02:23
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