CautionもしかしたらAMD Zen5 CPU（Ryzen 9000シリーズ）と相性が良くないかも？
gmpプログラム公式サイトの報告1によると、Ryzen9 9950X/Linux環境でGMPのプログラムを動かしていたら、CPUが逝ったそうです。しかも２台。AMDも公式に調査をしている模様2。Rのパッケージの方も影響があるかはわかりませんが、相性が悪い可能性もあるので、Zen5民の方はハードな使い方はしない方がいいかもしれないです。
Zen5故障問題はAsRock製マザボで起こりがちなのは聞いていましたが、今回はASUSマザボ+Noctuaクーラーだということで、ちょっと気になるところではあります。（最初、Noctua NH-U9Sで9950Xは無理じゃねと思ったのでNoctua公式サイト見に行ったら、medium turbo headroom判定だったのでびっくりしました。PBOも切っていたようですし、冷却面は問題なさそうです。となるとCPU本体かマザボの方か……）
packages
Contents
background
Youtubeを見ていたら、面白い動画が流れてきました。
2の108乗は十進法の表記で9を含まないそうです。しかも2の累乗で9を含まないもの最大の数らしい（未解決）。出典はオンライン整数大辞典3みたいですね。ということで確かめてみました。
problems
69の性質のときみたいにやってみます。とりあえず指数は300くらいまであれば十分でしょうか。
[1] 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 23 24 25 26 27 28
[25] 30 31 45 46 47 57 58 59 71 77 86 99 101 103 108 115 132 157 178 192 193 197 204 205
[49] 206 209 210 217 243 248 251 252 253 263 272 273 274 275 277 278 281 283 284 285 294想像よりも多くの数が残りました。多分コンピューター内部では2進数で計算してることと関係してるはずです。
Note処理の過程が見たい人向け
1. 2^(1:300) [1] 2.000000e+00 4.000000e+00 8.000000e+00 1.600000e+01 3.200000e+01 6.400000e+01 1.280000e+02
[8] 2.560000e+02 5.120000e+02 1.024000e+03 2.048000e+03 4.096000e+03 8.192000e+03 1.638400e+04
[15] 3.276800e+04 6.553600e+04 1.310720e+05 2.621440e+05 5.242880e+05 1.048576e+06 2.097152e+06
[22] 4.194304e+06 8.388608e+06 1.677722e+07 3.355443e+07 6.710886e+07 1.342177e+08 2.684355e+08
[29] 5.368709e+08 1.073742e+09 2.147484e+09 4.294967e+09 8.589935e+09 1.717987e+10 3.435974e+10
[36] 6.871948e+10 1.374390e+11 2.748779e+11 5.497558e+11 1.099512e+12 2.199023e+12 4.398047e+12
[43] 8.796093e+12 1.759219e+13 3.518437e+13 7.036874e+13 1.407375e+14 2.814750e+14 5.629500e+14
[50] 1.125900e+15 2.251800e+15 4.503600e+15 9.007199e+15 1.801440e+16 3.602880e+16 7.205759e+16
[57] 1.441152e+17 2.882304e+17 5.764608e+17 1.152922e+18 2.305843e+18 4.611686e+18 9.223372e+18
[64] 1.844674e+19 3.689349e+19 7.378698e+19 1.475740e+20 2.951479e+20 5.902958e+20 1.180592e+21
[71] 2.361183e+21 4.722366e+21 9.444733e+21 1.888947e+22 3.777893e+22 7.555786e+22 1.511157e+23
[78] 3.022315e+23 6.044629e+23 1.208926e+24 2.417852e+24 4.835703e+24 9.671407e+24 1.934281e+25
[85] 3.868563e+25 7.737125e+25 1.547425e+26 3.094850e+26 6.189700e+26 1.237940e+27 2.475880e+27
[92] 4.951760e+27 9.903520e+27 1.980704e+28 3.961408e+28 7.922816e+28 1.584563e+29 3.169127e+29
[99] 6.338253e+29 1.267651e+30 2.535301e+30 5.070602e+30 1.014120e+31 2.028241e+31 4.056482e+31
[106] 8.112964e+31 1.622593e+32 3.245186e+32 6.490371e+32 1.298074e+33 2.596148e+33 5.192297e+33
[113] 1.038459e+34 2.076919e+34 4.153837e+34 8.307675e+34 1.661535e+35 3.323070e+35 6.646140e+35
[120] 1.329228e+36 2.658456e+36 5.316912e+36 1.063382e+37 2.126765e+37 4.253530e+37 8.507059e+37
[127] 1.701412e+38 3.402824e+38 6.805647e+38 1.361129e+39 2.722259e+39 5.444518e+39 1.088904e+40
[134] 2.177807e+40 4.355614e+40 8.711229e+40 1.742246e+41 3.484491e+41 6.968983e+41 1.393797e+42
[141] 2.787593e+42 5.575186e+42 1.115037e+43 2.230075e+43 4.460149e+43 8.920298e+43 1.784060e+44
[148] 3.568119e+44 7.136238e+44 1.427248e+45 2.854495e+45 5.708991e+45 1.141798e+46 2.283596e+46
[155] 4.567193e+46 9.134385e+46 1.826877e+47 3.653754e+47 7.307508e+47 1.461502e+48 2.923003e+48
[162] 5.846007e+48 1.169201e+49 2.338403e+49 4.676805e+49 9.353610e+49 1.870722e+50 3.741444e+50
[169] 7.482888e+50 1.496578e+51 2.993155e+51 5.986311e+51 1.197262e+52 2.394524e+52 4.789049e+52
[176] 9.578097e+52 1.915619e+53 3.831239e+53 7.662478e+53 1.532496e+54 3.064991e+54 6.129982e+54
[183] 1.225996e+55 2.451993e+55 4.903986e+55 9.807971e+55 1.961594e+56 3.923189e+56 7.846377e+56
[190] 1.569275e+57 3.138551e+57 6.277102e+57 1.255420e+58 2.510841e+58 5.021681e+58 1.004336e+59
[197] 2.008673e+59 4.017345e+59 8.034690e+59 1.606938e+60 3.213876e+60 6.427752e+60 1.285550e+61
[204] 2.571101e+61 5.142202e+61 1.028440e+62 2.056881e+62 4.113761e+62 8.227523e+62 1.645505e+63
[211] 3.291009e+63 6.582018e+63 1.316404e+64 2.632807e+64 5.265615e+64 1.053123e+65 2.106246e+65
[218] 4.212492e+65 8.424983e+65 1.684997e+66 3.369993e+66 6.739987e+66 1.347997e+67 2.695995e+67
[225] 5.391989e+67 1.078398e+68 2.156796e+68 4.313591e+68 8.627183e+68 1.725437e+69 3.450873e+69
[232] 6.901746e+69 1.380349e+70 2.760699e+70 5.521397e+70 1.104279e+71 2.208559e+71 4.417118e+71
[239] 8.834235e+71 1.766847e+72 3.533694e+72 7.067388e+72 1.413478e+73 2.826955e+73 5.653911e+73
[246] 1.130782e+74 2.261564e+74 4.523128e+74 9.046257e+74 1.809251e+75 3.618503e+75 7.237006e+75
[253] 1.447401e+76 2.894802e+76 5.789604e+76 1.157921e+77 2.315842e+77 4.631684e+77 9.263367e+77
[260] 1.852673e+78 3.705347e+78 7.410694e+78 1.482139e+79 2.964277e+79 5.928555e+79 1.185711e+80
[267] 2.371422e+80 4.742844e+80 9.485688e+80 1.897138e+81 3.794275e+81 7.588550e+81 1.517710e+82
[274] 3.035420e+82 6.070840e+82 1.214168e+83 2.428336e+83 4.856672e+83 9.713344e+83 1.942669e+84
[281] 3.885338e+84 7.770676e+84 1.554135e+85 3.108270e+85 6.216540e+85 1.243308e+86 2.486616e+86
[288] 4.973232e+86 9.946465e+86 1.989293e+87 3.978586e+87 7.957172e+87 1.591434e+88 3.182869e+88
[295] 6.365737e+88 1.273147e+89 2.546295e+89 5.092590e+89 1.018518e+90 2.037036e+902. format(trim = TRUE, scientific = FALSE) [1] "2"
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[231] "3450873173395281893662608264862082200440622286464888248242066868668888"
[232] "6901746346790563787224206428624064400880244462828666486484022626226666"
[233] "13803492693581127574448402846248028800660488824646222862868044242442222"
[234] "27606985387162255148886804682486046600220866648282444624626088484884444"
[235] "55213970774324510396662608264862082200440622286464888248242066868668888"
[236] "110427941548649020692224206428624064400880244462828666486484022626226666"
[237] "220855883097298041284448402846248028800660488824646222862868044242442222"
[238] "441711766194596082468886804682486046600220866648282444624626088484884444"
[239] "883423532389192164826662608264862082200440622286464888248242066868668888"
[240] "1766847064778384329642224206428624064400880244462828666486484022626226666"
[241] "3533694129556768659284448402846248028800660488824646222862868044242442222"
[242] "7067388259113537318468886804682486046600220866648282444624626088484884444"
[243] "14134776518227074636826662608264862082200440622286464888248242066868668888"
[244] "28269553036454149272642224206428624064400880244462828666486484022626226666"
[245] "56539106072908298544284448402846248028800660488824646222862868044242442222"
[246] "113078212145816597098468886804682486046600220866648282444624626088484884444"
[247] "226156424291633194186826662608264862082200440622286464888248242066868668888"
[248] "452312848583266388362642224206428624064400880244462828666486484022626226666"
[249] "904625697166532776724284448402846248028800660488824646222862868044242442222"
[250] "1809251394333065553448468886804682486046600220866648282444624626088484884444"
[251] "3618502788666131107886826662608264862082200440622286464888248242066868668888"
[252] "7237005577332262214662642224206428624064400880244462828666486484022626226666"
[253] "14474011154664524428224284448402846248028800660488824646222862868044242442222"
[254] "28948022309329048856448468886804682486046600220866648282444624626088484884444"
[255] "57896044618658097712886826662608264862082200440622286464888248242066868668888"
[256] "115792089237316195424662642224206428624064400880244462828666486484022626226666"
[257] "231584178474632390848224284448402846248028800660488824646222862868044242442222"
[258] "463168356949264781786448468886804682486046600220866648282444624626088484884444"
[259] "926336713898529563462886826662608264862082200440622286464888248242066868668888"
[260] "1852673427797059126824662642224206428624064400880244462828666486484022626226666"
[261] "3705346855594118253648224284448402846248028800660488824646222862868044242442222"
[262] "7410693711188236507286448468886804682486046600220866648282444624626088484884444"
[263] "14821387422376473014462886826662608264862082200440622286464888248242066868668888"
[264] "29642774844752946038824662642224206428624064400880244462828666486484022626226666"
[265] "59285549689505892066648224284448402846248028800660488824646222862868044242442222"
[266] "118571099379011784122286448468886804682486046600220866648282444624626088484884444"
[267] "237142198758023568244462886826662608264862082200440622286464888248242066868668888"
[268] "474284397516047136488824662642224206428624064400880244462828666486484022626226666"
[269] "948568795032094272966648224284448402846248028800660488824646222862868044242442222"
[270] "1897137590064188545822286448468886804682486046600220866648282444624626088484884444"
[271] "3794275180128377091644462886826662608264862082200440622286464888248242066868668888"
[272] "7588550360256754183288824662642224206428624064400880244462828666486484022626226666"
[273] "15177100720513508367466648224284448402846248028800660488824646222862868044242442222"
[274] "30354201441027016734822286448468886804682486046600220866648282444624626088484884444"
[275] "60708402882054033468644462886826662608264862082200440622286464888248242066868668888"
[276] "121416805764108066936288824662642224206428624064400880244462828666486484022626226666"
[277] "242833611528216133862466648224284448402846248028800660488824646222862868044242442222"
[278] "485667223056432267724822286448468886804682486046600220866648282444624626088484884444"
[279] "971334446112864535548644462886826662608264862082200440622286464888248242066868668888"
[280] "1942668892225729071086288824662642224206428624064400880244462828666486484022626226666"
[281] "3885337784451458142062466648224284448402846248028800660488824646222862868044242442222"
[282] "7770675568902916284024822286448468886804682486046600220866648282444624626088484884444"
[283] "15541351137805832568048644462886826662608264862082200440622286464888248242066868668888"
[284] "31082702275611665136086288824662642224206428624064400880244462828666486484022626226666"
[285] "62165404551223330272062466648224284448402846248028800660488824646222862868044242442222"
[286] "124330809102446660544024822286448468886804682486046600220866648282444624626088484884444"
[287] "248661618204893321088048644462886826662608264862082200440622286464888248242066868668888"
[288] "497323236409786642166086288824662642224206428624064400880244462828666486484022626226666"
[289] "994646472819573284322062466648224284448402846248028800660488824646222862868044242442222"
[290] "1989292945639146568644024822286448468886804682486046600220866648282444624626088484884444"
[291] "3978585891278293137288048644462886826662608264862082200440622286464888248242066868668888"
[292] "7957171782556586275466086288824662642224206428624064400880244462828666486484022626226666"
[293] "15914343565113172550822062466648224284448402846248028800660488824646222862868044242442222"
[294] "31828687130226345100644024822286448468886804682486046600220866648282444624626088484884444"
[295] "63657374260452690200288048644462886826662608264862082200440622286464888248242066868668888"
[296] "127314748520905380400466086288824662642224206428624064400880244462828666486484022626226666"
[297] "254629497041810760800822062466648224284448402846248028800660488824646222862868044242442222"
[298] "509258994083621521600644024822286448468886804682486046600220866648282444624626088484884444"
[299] "1018517988167243043200288048644462886826662608264862082200440622286464888248242066868668888"
[300] "2037035976334486086400466086288824662642224206428624064400880244462828666486484022626226666"3. grep(pattern = "9", x = ., invert = TRUE) [1] 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 23 24 25 26 27 28
[25] 30 31 45 46 47 57 58 59 71 77 86 99 101 103 108 115 132 157 178 192 193 197 204 205
[49] 206 209 210 217 243 248 251 252 253 263 272 273 274 275 277 278 281 283 284 285 294solution
gmp package
というわけで、非常に大きな数でも正確に計算してくれるパッケージであるgmpを試してみます。様々なプログラミング言語で使えるようです。任意の長さの整数や有理数、浮動小数点に対応しているそうです。
gmp::as.bigz()で任意の数をbiz.zクラスの整数にできます。引数aにはintかdbl、chrがいれられて、chrの場合は0x始まりで16進数、0bで2進数、0で8進数、0のprefixなしで10進数扱いになるようです。
Big Integer ('bigz') :
[1] 2Big Integer ('bigz') :
[1] 3Big Integer ('bigz') :
[1] 255演算は普通の演算子でもできますし関数でもできます。
Big Integer ('bigz') :
[1] 5Big Integer ('bigz') :
[1] 5無料大数も作れます。
Big Integer ('bigz') :
[1] 10000000000000000000000000000000000000000000000000000000000000000Big Integer ('bigz') :
[1] 10000000000000000000000000000000000000000000000000000000000000000[1] 6410の64乗なので0が64個でOKですね。
gmp::as.bigq(n, d)は、なんとnが分子でdが分母の分数を約分してくれます。計算もOK。
Big Rational ('bigq') :
[1] 1/5Big Rational ('bigq') :
[1] 1/2他にも、階乗を計算してくれたり、素因数分解してくれたり、baseの関数と同じ働きをしてくれる関数があったりします。
solution
というわけで本題に戻ります。上記の例にも挙げましたが、指数はbig.zクラスじゃなくても大丈夫なようなので、2だけbigz整数にして計算します。
[1] 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 23 24 25 26 27 28
[25] 30 31 45 46 47 57 58 59 71 77 99 108こちらはうまくいきました。
Note処理の過程が見たい人向け
1. gmp::as.bigz(2)^(1:300)Big Integer ('bigz') object of length 300:
[1] 2
[2] 4
[3] 8
[4] 16
[5] 32
[6] 64
[7] 128
[8] 256
[9] 512
[10] 1024
[11] 2048
[12] 4096
[13] 8192
[14] 16384
[15] 32768
[16] 65536
[17] 131072
[18] 262144
[19] 524288
[20] 1048576
[21] 2097152
[22] 4194304
[23] 8388608
[24] 16777216
[25] 33554432
[26] 67108864
[27] 134217728
[28] 268435456
[29] 536870912
[30] 1073741824
[31] 2147483648
[32] 4294967296
[33] 8589934592
[34] 17179869184
[35] 34359738368
[36] 68719476736
[37] 137438953472
[38] 274877906944
[39] 549755813888
[40] 1099511627776
[41] 2199023255552
[42] 4398046511104
[43] 8796093022208
[44] 17592186044416
[45] 35184372088832
[46] 70368744177664
[47] 140737488355328
[48] 281474976710656
[49] 562949953421312
[50] 1125899906842624
[51] 2251799813685248
[52] 4503599627370496
[53] 9007199254740992
[54] 18014398509481984
[55] 36028797018963968
[56] 72057594037927936
[57] 144115188075855872
[58] 288230376151711744
[59] 576460752303423488
[60] 1152921504606846976
[61] 2305843009213693952
[62] 4611686018427387904
[63] 9223372036854775808
[64] 18446744073709551616
[65] 36893488147419103232
[66] 73786976294838206464
[67] 147573952589676412928
[68] 295147905179352825856
[69] 590295810358705651712
[70] 1180591620717411303424
[71] 2361183241434822606848
[72] 4722366482869645213696
[73] 9444732965739290427392
[74] 18889465931478580854784
[75] 37778931862957161709568
[76] 75557863725914323419136
[77] 151115727451828646838272
[78] 302231454903657293676544
[79] 604462909807314587353088
[80] 1208925819614629174706176
[81] 2417851639229258349412352
[82] 4835703278458516698824704
[83] 9671406556917033397649408
[84] 19342813113834066795298816
[85] 38685626227668133590597632
[86] 77371252455336267181195264
[87] 154742504910672534362390528
[88] 309485009821345068724781056
[89] 618970019642690137449562112
[90] 1237940039285380274899124224
[91] 2475880078570760549798248448
[92] 4951760157141521099596496896
[93] 9903520314283042199192993792
[94] 19807040628566084398385987584
[95] 39614081257132168796771975168
[96] 79228162514264337593543950336
[97] 158456325028528675187087900672
[98] 316912650057057350374175801344
[99] 633825300114114700748351602688
[100] 1267650600228229401496703205376
[101] 2535301200456458802993406410752
[102] 5070602400912917605986812821504
[103] 10141204801825835211973625643008
[104] 20282409603651670423947251286016
[105] 40564819207303340847894502572032
[106] 81129638414606681695789005144064
[107] 162259276829213363391578010288128
[108] 324518553658426726783156020576256
[109] 649037107316853453566312041152512
[110] 1298074214633706907132624082305024
[111] 2596148429267413814265248164610048
[112] 5192296858534827628530496329220096
[113] 10384593717069655257060992658440192
[114] 20769187434139310514121985316880384
[115] 41538374868278621028243970633760768
[116] 83076749736557242056487941267521536
[117] 166153499473114484112975882535043072
[118] 332306998946228968225951765070086144
[119] 664613997892457936451903530140172288
[120] 1329227995784915872903807060280344576
[121] 2658455991569831745807614120560689152
[122] 5316911983139663491615228241121378304
[123] 10633823966279326983230456482242756608
[124] 21267647932558653966460912964485513216
[125] 42535295865117307932921825928971026432
[126] 85070591730234615865843651857942052864
[127] 170141183460469231731687303715884105728
[128] 340282366920938463463374607431768211456
[129] 680564733841876926926749214863536422912
[130] 1361129467683753853853498429727072845824
[131] 2722258935367507707706996859454145691648
[132] 5444517870735015415413993718908291383296
[133] 10889035741470030830827987437816582766592
[134] 21778071482940061661655974875633165533184
[135] 43556142965880123323311949751266331066368
[136] 87112285931760246646623899502532662132736
[137] 174224571863520493293247799005065324265472
[138] 348449143727040986586495598010130648530944
[139] 696898287454081973172991196020261297061888
[140] 1393796574908163946345982392040522594123776
[141] 2787593149816327892691964784081045188247552
[142] 5575186299632655785383929568162090376495104
[143] 11150372599265311570767859136324180752990208
[144] 22300745198530623141535718272648361505980416
[145] 44601490397061246283071436545296723011960832
[146] 89202980794122492566142873090593446023921664
[147] 178405961588244985132285746181186892047843328
[148] 356811923176489970264571492362373784095686656
[149] 713623846352979940529142984724747568191373312
[150] 1427247692705959881058285969449495136382746624
[151] 2854495385411919762116571938898990272765493248
[152] 5708990770823839524233143877797980545530986496
[153] 11417981541647679048466287755595961091061972992
[154] 22835963083295358096932575511191922182123945984
[155] 45671926166590716193865151022383844364247891968
[156] 91343852333181432387730302044767688728495783936
[157] 182687704666362864775460604089535377456991567872
[158] 365375409332725729550921208179070754913983135744
[159] 730750818665451459101842416358141509827966271488
[160] 1461501637330902918203684832716283019655932542976
[161] 2923003274661805836407369665432566039311865085952
[162] 5846006549323611672814739330865132078623730171904
[163] 11692013098647223345629478661730264157247460343808
[164] 23384026197294446691258957323460528314494920687616
[165] 46768052394588893382517914646921056628989841375232
[166] 93536104789177786765035829293842113257979682750464
[167] 187072209578355573530071658587684226515959365500928
[168] 374144419156711147060143317175368453031918731001856
[169] 748288838313422294120286634350736906063837462003712
[170] 1496577676626844588240573268701473812127674924007424
[171] 2993155353253689176481146537402947624255349848014848
[172] 5986310706507378352962293074805895248510699696029696
[173] 11972621413014756705924586149611790497021399392059392
[174] 23945242826029513411849172299223580994042798784118784
[175] 47890485652059026823698344598447161988085597568237568
[176] 95780971304118053647396689196894323976171195136475136
[177] 191561942608236107294793378393788647952342390272950272
[178] 383123885216472214589586756787577295904684780545900544
[179] 766247770432944429179173513575154591809369561091801088
[180] 1532495540865888858358347027150309183618739122183602176
[181] 3064991081731777716716694054300618367237478244367204352
[182] 6129982163463555433433388108601236734474956488734408704
[183] 12259964326927110866866776217202473468949912977468817408
[184] 24519928653854221733733552434404946937899825954937634816
[185] 49039857307708443467467104868809893875799651909875269632
[186] 98079714615416886934934209737619787751599303819750539264
[187] 196159429230833773869868419475239575503198607639501078528
[188] 392318858461667547739736838950479151006397215279002157056
[189] 784637716923335095479473677900958302012794430558004314112
[190] 1569275433846670190958947355801916604025588861116008628224
[191] 3138550867693340381917894711603833208051177722232017256448
[192] 6277101735386680763835789423207666416102355444464034512896
[193] 12554203470773361527671578846415332832204710888928069025792
[194] 25108406941546723055343157692830665664409421777856138051584
[195] 50216813883093446110686315385661331328818843555712276103168
[196] 100433627766186892221372630771322662657637687111424552206336
[197] 200867255532373784442745261542645325315275374222849104412672
[198] 401734511064747568885490523085290650630550748445698208825344
[199] 803469022129495137770981046170581301261101496891396417650688
[200] 1606938044258990275541962092341162602522202993782792835301376
[201] 3213876088517980551083924184682325205044405987565585670602752
[202] 6427752177035961102167848369364650410088811975131171341205504
[203] 12855504354071922204335696738729300820177623950262342682411008
[204] 25711008708143844408671393477458601640355247900524685364822016
[205] 51422017416287688817342786954917203280710495801049370729644032
[206] 102844034832575377634685573909834406561420991602098741459288064
[207] 205688069665150755269371147819668813122841983204197482918576128
[208] 411376139330301510538742295639337626245683966408394965837152256
[209] 822752278660603021077484591278675252491367932816789931674304512
[210] 1645504557321206042154969182557350504982735865633579863348609024
[211] 3291009114642412084309938365114701009965471731267159726697218048
[212] 6582018229284824168619876730229402019930943462534319453394436096
[213] 13164036458569648337239753460458804039861886925068638906788872192
[214] 26328072917139296674479506920917608079723773850137277813577744384
[215] 52656145834278593348959013841835216159447547700274555627155488768
[216] 105312291668557186697918027683670432318895095400549111254310977536
[217] 210624583337114373395836055367340864637790190801098222508621955072
[218] 421249166674228746791672110734681729275580381602196445017243910144
[219] 842498333348457493583344221469363458551160763204392890034487820288
[220] 1684996666696914987166688442938726917102321526408785780068975640576
[221] 3369993333393829974333376885877453834204643052817571560137951281152
[222] 6739986666787659948666753771754907668409286105635143120275902562304
[223] 13479973333575319897333507543509815336818572211270286240551805124608
[224] 26959946667150639794667015087019630673637144422540572481103610249216
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[237] "220855883097298041197912187592864814478435487109452369765200775161577472"
[238] "441711766194596082395824375185729628956870974218904739530401550323154944"
[239] "883423532389192164791648750371459257913741948437809479060803100646309888"
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[241] "3533694129556768659166595001485837031654967793751237916243212402585239552"
[242] "7067388259113537318333190002971674063309935587502475832486424805170479104"
[243] "14134776518227074636666380005943348126619871175004951664972849610340958208"
[244] "28269553036454149273332760011886696253239742350009903329945699220681916416"
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[250] "1809251394333065553493296640760748560207343510400633813116524750123642650624"
[251] "3618502788666131106986593281521497120414687020801267626233049500247285301248"
[252] "7237005577332262213973186563042994240829374041602535252466099000494570602496"
[253] "14474011154664524427946373126085988481658748083205070504932198000989141204992"
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[255] "57896044618658097711785492504343953926634992332820282019728792003956564819968"
[256] "115792089237316195423570985008687907853269984665640564039457584007913129639936"
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[261] "3705346855594118253554271520278013051304639509300498049262642688253220148477952"
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[263] "14821387422376473014217086081112052205218558037201992197050570753012880593911808"
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[288] "497323236409786642155382248146820840100456150797347717440463976893159497012533375533056"
[289] "994646472819573284310764496293641680200912301594695434880927953786318994025066751066112"
[290] "1989292945639146568621528992587283360401824603189390869761855907572637988050133502132224"
[291] "3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448"
[292] "7957171782556586274486115970349133441607298412757563479047423630290551952200534008528896"
[293] "15914343565113172548972231940698266883214596825515126958094847260581103904401068017057792"
[294] "31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584"
[295] "63657374260452690195888927762793067532858387302060507832379389042324415617604272068231168"
[296] "127314748520905380391777855525586135065716774604121015664758778084648831235208544136462336"
[297] "254629497041810760783555711051172270131433549208242031329517556169297662470417088272924672"
[298] "509258994083621521567111422102344540262867098416484062659035112338595324940834176545849344"
[299] "1018517988167243043134222844204689080525734196832968125318070224677190649881668353091698688"
[300] "2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376"3. grep(pattern = "9", x = ., invert = TRUE) [1] 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 23 24 25 26 27 28
[25] 30 31 45 46 47 57 58 59 71 77 99 108helpや公式サイト4によるとPCのRAMの容量にしか制限されないみたいなので、もっと大きな数も行けそうです。ということで試しに指数を10000まで増やして試してみます。
[1] 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 23 24 25 26 27 28
[25] 30 31 45 46 47 57 58 59 71 77 99 108先ほどと同じ結果が返ってきました。ちなみにこのあと指数の方を1:100000にしても同じ結果が返ってきたのですが、Rstudioが表示しているRAMのセッション使用量が378MiBから2.4GiBになって、処理に20秒ほどかかりました。コンピューターインテンシブな処理です。
Conclusion
2の108乗の10進数表記には9が現れないということを標準のRでは確かめられなかったので、gmpパッケージを使って確かめてみました。
自分の領域だとお世話になる場面があまり思いつきませんが、知っていて損はないはずと思いました。
Session Infomation
Notesessioninfo
R version 4.5.2 (2025-10-31 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26100)
Matrix products: default
LAPACK version 3.12.1
locale:
[1] LC_COLLATE=Japanese_Japan.utf8 LC_CTYPE=Japanese_Japan.utf8 LC_MONETARY=Japanese_Japan.utf8
[4] LC_NUMERIC=C LC_TIME=Japanese_Japan.utf8
time zone: Asia/Tokyo
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] gmp_0.7-5 lubridate_1.9.5 forcats_1.0.1 stringr_1.6.0 dplyr_1.2.0 purrr_1.2.1
[7] readr_2.1.6 tidyr_1.3.2 tibble_3.3.1 ggplot2_4.0.2 tidyverse_2.0.0
loaded via a namespace (and not attached):
[1] gtable_0.3.6 jsonlite_2.0.0 compiler_4.5.2 tidyselect_1.2.1
[5] systemfonts_1.3.1 scales_1.4.0 textshaping_1.0.4 yaml_2.3.12
[9] fastmap_1.2.0 R6_2.6.1 labeling_0.4.3 generics_0.1.4
[13] knitr_1.51 htmlwidgets_1.6.4 tzdb_0.5.0 pillar_1.11.1
[17] RColorBrewer_1.1-3 rlang_1.1.7 stringi_1.8.7 xfun_0.56
[21] ViewPipeSteps_0.1.0 S7_0.2.1 otel_0.2.0 timechange_0.4.0
[25] cli_3.6.5 withr_3.0.2 magrittr_2.0.4 digest_0.6.39
[29] grid_4.5.2 rstudioapi_0.18.0 hms_1.1.4 lifecycle_1.0.5
[33] vctrs_0.7.1 evaluate_1.0.5 glue_1.8.0 farver_2.1.2
[37] ragg_1.5.0 pacman_0.5.1 rmarkdown_2.30 tools_4.5.2
[41] pkgconfig_2.0.3 htmltools_0.5.9