Embedded Primes

(May 1st, 2010)

 

Hello SeqFans,

 

a(n) > a(n-1) and a(n) is the smallest available composite embedding the smallest not yet embedded prime:

 

S = 12,30,35,57,110,130,170,190,230,290,310,370,410,430,447,453,...

p =  2 3   5  7 11  13  17  19  23  29  31  37  41  43   47  53 ...

 

Could please someone compute a hundred terms or so, rephrase my definition in good English, coauthor and submit (if of

interest)?

 

Thanks,

É.

 

---

 

A couple of days later, Jean-Marc Falcoz sent me the three lists hereunder (of embedded primes):

 

« Voici la liste des 10000 premiers éléments de ta suite, et plus bas, la même liste, mais pour chaque élément, on a aussi le nombre premier enchâssé ;

 

   liste1.txt est un gros fichier texte constitué de la liste des 10000 premiers éléments, soit :

   {12,30,35,57,110,130,170,190,230,290,310,370,410,430,447,453,459,561...}

   dans le même fichier, plus loin, on a la même liste, avec chaque nombre accompagné de son nombre premier, soit :

   {{12,2},{30,3},{35,5},{57,7},{110,11},{130,13},{170,17},{190,19},{230,23},{290,29},...} »

 

Dans liste2.txt, je n'ai gardé que les éléments les plus intéressants, soit ceux qui ne finissent pas par 0 (il n'y en a que 93 parmi les 30000 premiers éléments de la suite), j'ai gardé le même format, soit :

 

{12,35,57,447,453,459,561,567,671,779,783,789,897,1113,1127...

 

et

 

{{12,2},{35,5},{57,7},{447,47},{453,53},{459,59},{561,61},{567,67},{671,71},{779,79},... »

 

Thank you Jean-Marc !

 

S = {12, 30, 35, 57, 110, 130, 170, 190, 230, 290, 310, 370, 410, 430, 447, 453, 459, 561, 567, 671, 730, 779, 783, 789, 897, 1010, 1030, 1070, 1090, 1113, 1127, 1131, 1137, 1139, 1149, 1510, 1570, 1630, 1670, 1730, 1790, 1810, 1910, 1930, 1970, 1990, 2110, 2223, 2227, 2229, 2233, 2390, 2410, 2510, 2570, 2630, 2690, 2710, 2770, 2810, 2830, 2930, 3070, 3110, 3130, 3170, 3310, 3337, 3470, 3490, 3530, 3590, 3670, 3730, 3790, 3830, 3890, 3970, 4010, 4090, 4190, 4210, 4310, 4330, 4390, 4430, 4449, 4570, 4610, 4630, 4670, 4790, 4870, 4910, 4990, 5030, 5090, 5210, 5230, 5410, 5470, 5570, 5630, 5690, 5710, 5770, 5870, 5930, 5990, 6010, 6070, 6130, 6170, 6190, 6310, 6410, 6430, 6470, 6530, 6590, 6610, 6730, 6770, 6830, 6910, 7010, 7090, 7190, 7270, 7330, 7390, 7430, 7510, 7570, 7610, 7690, 7730, 7787, 7797, 7809, 7811, 7821, 8230, 8270, 8290, 8390, 8530, 8570, 8590, 8630, 8770, 8810, 8830, 8870, 8907, 8911, 8919, 9290, 9370, 9410, 9470, 9530, 9670, 9710, 9770, 9830, 9910, 9970, 10090, 10130, 10190, 10210, 10310, 10330, 10390, 10490, 10510, 10610, 10630, 10690, 10870, 10910, 10930, 10970, 11030, 11090, 11170, 11230, 11290, 11510, 11530, 11630, 11710, 11810, 11870, 11930, 12010, 12130, 12170, 12230, 12290, 12310, 12370, 12490, 12590, 12770, 12790, 12830, 12890, 12910, 12970, 13010, 13030, 13070, 13190, 13210, 13270, 13610, 13670, 13730, 13810, 13990, 14090, 14230, 14270, 14290, 14330, 14390, 14470, 14510, 14530, 14590, 14710, 14810, 14830, 14870, 14890, 14930, 14990, 15110, 15230, 15310, 15430, 15490, 15530, 15590, 15670, 15710, 15790, 15830, 15970, 16010, 16070, 16090, 16130, 16190, 16210, 16270, 16370, 16570, 16630, 16670, 16690, 16930, 16970, 16990, 17090, 17210, 17230, 17330, 17410, 17470, 17530, 17590, 17770, 17830, 17870, 17890, 18010, 18110, 18230, 18310, 18470, 18610, 18670, 18710, 18730, 18770, 18790, 18890, 19010, 19070, 19130, 19310, 19330, 19490, 19510, 19730, 19790, 19870, 19930, 19970, 19990, 20030, 20110, 20170, 20270, 20290, 20390, 20530, 20630, 20690, 20810, 20830, 20870, 20890, 20990, 21110, 21130, 21290, 21310, 21370, 21410, 21430, 21530, 21610, 21790, 22030, 22070, 22130, 22210, 22237, 22239, 22243, 22251, 22267, 22269, 22730, 22810, 22870, 22930, 22970, 23090, 23110, 23330, 23390, 23410, 23470, 23510, 23570, 23710, 23770, 23810, 23830, 23890, 23930, 23990, 24110, 24170, 24230, 24370, 24410, 24470, 24590, 24670, 24730, 24770, 25030, 25210, 25310, 25390, 25430, 25490, 25510, 25570, 25790, 25910, 25930, 26090, 26170, 26210, 26330, 26470, 26570, 26590, 26630, 26710, 26770, 26830, 26870, 26890, 26930, 26990, 27070, 27110, 27130, 27190, 27290, 27310, 27410, 27490, 27530, 27670, 27770, 27890, 27910, 27970, 28010, 28030, 28190, 28330, 28370, 28430, 28510, 28570, 28610, 28790, 28870, 28970, 29030, 29090, 29170, 29270, 29390, 29530, 29570, 29630, 29690, 29710, 29990, 30010, 30110, 30190, 30230, 30370, 30410, 30490, 30610, 30670, 30790, 30830, 30890, 31090, 31190, 31210, 31370, 31630, 31670, 31690, 31810, 31870, 31910, 32030, 32090, 32170, 32210, 32290, 32510, 32530, 32570, 32590, 32710, 32990, 33010, 33070, 33130, 33190, 33230, 33290, 33310, 33430, 33470, 33590, 33610, 33710, 33730, 33890, 33910, 34070, 34130, 34330, 34490, 34570, 34610, 34630, 34670, 34690, 34910, 34990, 35110, 35170, 35270, 35290, 35330, 35390, 35410, 35470, 35570, 35590, 35710, 35810, 35830, 35930, 36070, 36130, 36170, 36230, 36310, 36370, 36430, 36590, 36710, 36730, 36770, 36910, 36970, 37010, 37090, 37190, 37270, 37330, 37390, 37610, 37670, 37690, 37790, 37930, 37970, 38030, 38210, 38230, 38330, 38470, 38510, 38530, 38630, 38770, 38810, 38890, 39070, 39110, 39170, 39190, 39230, 39290, 39310, 39430, 39470, 39670, 39890, 40010, 40030, 40070, 40130, 40190, 40210, 40270, 40490, 40510, 40570, 40730, 40790, 40910, 40930, 40990, 41110, 41270, 41290, 41330, 41390, 41530, 41570, 41590, 41770, 42010, 42110, 42170, 42190, 42290, 42310, 42410, 42430, 42530, 42590, 42610, 42710, 42730, 42830, 42890, 42970, 43270, 43370, 43390, 43490, 43570, 43630, 43730, 43910, 43970, 44090, 44210, 44230, 44410, 44447, 44451, 44457, 44463, 44481, 44830, 44930, 45070, 45130, 45170, 45190, 45230, 45470, 45490, 45610, 45670, 45830, 45910, 45970, 46030, 46210, 46370, 46390, 46430, 46490, 46510, 46570, 46630, 46730, 46790, 46910, 47030, 47210, 47230, 47290, 47330, 47510, 47590, 47830, 47870, 47890, 47930, 47990, 48010, 48130, 48170, 48310, 48610, 48710, 48770, 48890, 49030, 49090, 49190, 49310, 49330, 49370, 49430, 49510, 49570, 49670, 49690, 49730, 49870, 49930, 49990, 50030, 50090, 50110, 50210, 50230, 50390, 50510, 50590, 50770, 50810, 50870, 50990, 51010, 51070, 51130, 51190, 51470, 51530, 51670, 51710, 51790, 51890, 51970, 52090, 52270, 52310, 52330, 52370, 52610, 52730, 52790, 52810, 52970, 53030, 53090, 53230, 53330, 53470, 53510, 53810, 53870, 53930, 53990, 54070, 54130, 54170, 54190, 54310, 54370, 54410, 54430, 54490, 54710, 54770, 54790, 54830, 55010, 55030, 55070, 55190, 55210, 55270, 55310, 55557, 55563, 55569, 55573, 55581, 55591, 55623, 56390, 56410, 56470, 56510, 56530, 56570, 56590, 56690, 56830, 56890, 56930, 57010, 57110, 57170, 57370, 57410, 57430, 57490, 57790, 57830, 57910, 58010, 58070, 58130, 58210, 58270, 58390, 58430, 58490, 58510, 58570, 58610, 58670, 58690, 58790, 58810, 58970, 59030, 59230, 59270, 59390, 59530, 59810, 59870, 60070, 60110, 60290, 60370, 60430, 60470, 60530, 60670, 60730, 60790, 60890, 60910, 61010, 61130, 61210, 61310, 61330, 61430, 61510, 61630, 61730, 61970, 61990, 62030, 62110, 62170, 62210, 62290, 62470, 62570, 62630, 62690, 62710, 62770, 62870, 62990, 63010, 63110, 63170, 63230, 63290, 63370, 63430, 63530, 63590, 63610, 63670, 63730, 63790, 63890, 63970, 64210, 64270, 64490, 64510, 64690, 64730, 64810, 64910, 65210, 65290, 65470, 65510, 65530, 65630, 65690, 65710, 65770, 65810, 65990, 66070, 66190, 66370, 66530, 66590, 66610, 66673, 66679, 66689, 66691, 67010, 67030, 67090, 67190, 67330, 67370, 67610, 67630, 67790, 67810, 67910, 67930, 68030, 68230, 68270, 68290, 68330, 68410, 68570, 68630, 68690, 68710, 68830, 68990, 69070, 69110, 69170, 69470, 69490, 69590, 69610, 69670, 69710, 69770, 69830, 69910, 69970, 70010, 70130, 70190, 70270, 70390, 70430, 70570, 70690, 70790, 71030, 71090, 71210, 71270, 71290, 71510, 71590, 71770, 71870, 71930, 72070, 72110, 72130, 72190, 72290, 72370, 72430, 72470, 72530, 72830, 72970, 73070, 73090, 73210, 73310, 73330, 73490, 73510, 73690, 73930, 74110, 74170, 74330, 74510, 74570, 74590, 74770, 74810, 74870, 74890, 74990, 75070, 75170, 75230, 75290, 75370, 75410, 75470, 75490, 75590, 75610, 75730, 75770, 75830, 75890, 75910, 76030, 76070, 76210, 76390, 76430, 76490, 76690, 76730, 76810, 76870, 76910, 76990, 77030, 77170, 77230, 77270, 77410, 77530, 77570, 77590, 77789, 77793, 77817, 77823, 77829, 77841, 77853, 78670, 78730, 78770, 78790, 78830, 79010, 79070, 79190, 79270, 79330, 79370, 79490, 79510, 79630, 79930, 80090, 80110, 80170, 80390, 80530, 80590, 80690, 80810, 80870, 80890, 80930, 81010, 81110, 81170, 81230, 81470, 81610, 81670, 81710, 81790, 81910, 82090, 82190, 82210, 82310, 82330, 82370, 82430, 82630, 82690, 82730, 82870, 82910, 82930, 82970, 83110, 83170, 83290, 83530, 83630, 83690, 83770, 83870, 83890, 84190, 84230, 84290, 84310, 84430, 84470, 84610, 84670, 85010, 85130, 85210, 85270, 85370, 85390, 85430, 85630, 85730, 85810, 85970, 85990, 86090, 86230, 86270, 86290, 86410, 86470, 86630, 86690, 86770, 86810, 86890, 86930, 86990, 87070, 87130, 87190, 87310, 87370, 87410, 87470, 87530, 87610, 87790, 87830, 88030, 88070, 88190, 88210, 88310, 88370, 88390, 88490, 88610, 88630, 88670, 88870, 88893, 88923, 88929, 88933, 88941, 89510, 89630, 89690, 89710, 89990, 90010, 90070, 90110, 90130, 90290, 90410, 90430, 90490, 90590, 90670, 90910, 91030, 91090, 91270, 91330, 91370, 91510, 91570, 91610, 91730, 91810, 91870, 91990, 92030, 92090, 92210, 92270, 92390, 92410, 92570, 92770, 92810, 92830, 92930, 93110, 93190, 93230, 93370, 93410, 93430, 93490, 93710, 93770, 93910, 93970, 94030, 94130, 94190, 94210, 94310, 94330, 94370, 94390, 94610, 94630, 94670, 94730, 94790, 94910, 94970, 95110, 95210, 95330, 95390, 95470, 95510, 95870, 96010, 96130, 96190, 96230, 96290, 96310, 96430, 96490, 96610, 96770, 96790, 96890, 96970, 97190, 97210, 97330, 97390, 97430, 97490, 97670, 97690, 97810, 97870, 97910, 98030, 98110, 98170, 98290, 98330, 98390, 98510, 98570, 98590, 98710, 98830, 98870, 99010, 99070, 99230, 99290, 99310, 99410, 99490, 99670, 99730, 100070, 100090, 100370, 100390, 100610, 100670, 100690, 100790, 100910, 100930, 100990, 101030, 101110, 101330, 101390, 101410, 101510, 101590, 101630, 101690, 101770, 101810, 101930, 102110, 102230, 102430, 102470, 102530, 102590, 102670, 102710, 102730, 102890, 103010, 103030, 103130, 103210, 103310, 103330, 103370, 103430, 103570, 103690, 103910, 103990, 104270, 104290, 104330, 104530, 104570, 104590, 104630, 104770, 104870, 104990, 105010, 105130, 105290, 105310, 105590, 105670, 105890, 105970, 106010, 106070, 106130, 106270, 106310, 106390, 106510, 106570, 106630, 106670, 106870, 106910, 107090, 107110, 107230, 107290, 107330, 107390, 107530, 107710, 107810, 107890, 107990, 108310, 108370, 108470, 108530, 108590, 108610, 108670, 108830, 108890, 108910, 109030, 109090, 109370, 109390, 109490, 109570, 109730, 109790, 109870, 109930, 110030, 110270, 110470, 110570, 110590, 110690, 110710, 110830, 110870, 110930, 111113, 111117, 111190, 111310, 111490, 111590, 111610, 111710, 111730, 111770, 111970, 112130, 112390, 112430, 112510, 112570, 112610, 112730, 112790, 112870, 112990, 113110, 113170, 113210, 113290, 113510, 113530, 113690, 113830, 113930, 113990, 114110, 114230, 114370, 114430, 114470, 114670, 114710, 114830, 114890, 114910, 114970, 115030, 115190, 115270, 115490, 115510, 115790, 115870, 115930, 115970, 116170, 116210, 116330, 116570, 116770, 116810, 116890, 116990, 117010, 117170, 117190, 117310, 117430, 117770, 117790, 117830, 117890, 118010, 118070, 118130, 118210, 118270, 118310, 118330, 118390, 118630, 118670, 118870, 118970, 119030, 119090, 119230, 119270, 119330, 119390, 119410, 119530, 119590, 119690, 119710, 119810, 119870, 120070, 120110, 120370, 120410, 120430, 120490, 120710, 120730, 120970, 121010, 121070, 121090, 121130, 121190, 121430, 121490, 121570, 121610, 121630, 121970, 122030, 122110, 122270, 122390, 122410, 122510, 122530, 122630, 122690, 122770, 122810, 122890, 123010, 123230, 123290, 123430, 123470, 123730, 123770, 123790, 123910, 124010, 124090, 124130, 124210, 124330, 124370, 124510, 124570, 124730, 124790, 124870, 124910, 124970, 125030, 125110, 125170, 125270, 125390, 125410, 125470, 125530, 125690, 125770, 125830, 125890, 126010, 126110, 126130, 126190, 126370, 126410, 126470, 126530, 126590, 126710, 126890, 126970, 127030, 127130, 127210, 127390, 127430, 127570, 127630, 127810, 127910, 127990, 128090, 128210, 128230, 128290, 128410, 128530, 128890, 128930, 128990, 129070, 129110, 129170, 129190, 129230, 129410, 129530, 129590, 129670, 129730, 129790, 129830, 130010, 130030, 130070, 130090, 130330, 130370, 130430, 130490, 130630, 130930, 130990, 131030, 131090, 131210, 131270, 131470, 131510, 131590, 131630, 131710, 131770, 131830, 131870, 132170, 132190, 132290, 132410, 132490, 132590, 132670, 132910, 132970, 133090, 133130, 133270, 133310, 133370, 133390, 133670, 133810, 133970, 133990, 134110, 134170, 134210, 134410, 134510, 134570, 134630, 134690, 134770, 134870, 134990, 135130, 135230, 135370, 135530, 135670, 135770, 135910, 135970, 136130, 136190, 136270, 136330, 136490, 136690, 136790, 136810, 136870, 136910, 136930, 136970, 137090, 137110, 137210, 137230, 137290, 137510, 137570, 137590, 137630, 137810, 137890, 137990, 138070, 138290, 138310, 138410, 138590, 138730, 138770, 138790, 138830, 139010, 139030, 139070, 139130, 139210, 139310, 139330, 139630, 139670, 139970, 139990, 140090, 140110, 140290, 140330, 140510, 140570, 140710, 140810, 140830, 140870, 141070, 141430, 141490, 141530, 141590, 141730, 141770, 141970, 142070, 142210, 142430, 142490, 142510, 142810, 142930, 143030, 143210, 143230, 143270, 143410, 143470, 143690, 143870, 143890, 144010, 144070, 144110, 144190, 144230, 144310, 144370, 144470, 144490, 144610, 144790, 144890, 145030, 145190, 145330, 145370, 145430, 145490, 145510, 145570, 145610, 145630, 145910, 145930, 146210, 146270, 146290, 146330, 146390, 146530, 146570, 146690, 146830, 146990, 147130, 147170, 147230, 147310, 147370, 147410, 147470, 147530, 147590, 147670, 147710, 147790, 147830, 147970, 148130, 148210, 148270, 148310, 148430, 148510, 148670, 148690, 148790, 148870, 148910, 148970, 149230, 149290, 149390, 149470, 149510, 149570, 149690, 149830, 150130, 150170, 150310, 150530, 150610, 150730, 150770, 150830, 150910, 151010, 151070, 151210, 151310, 151370, 151390, 151490, 151610, 151730, 151870, 151930, 151990, 152170, 152270, 152330, 152410, 152590, 152630, 152690, 152710, 152770, 152870, 152890, 152990, 153070, 153130, 153190, 153290, 153310, 153490, 153590, 153610, 153730, 153770, 153830, 153910, 154010, 154130, 154270, 154390, 154430, 154510, 154610, 154670, 154730, 154930, 154970, 155110, 155270, 155410, 155510, 155590, 155690, 155810, 155830, 156010, 156070, 156190, 156290, 156410, 156430, 156470, 156490, 156610, 156670, 156710, 156790, 156830, 157270, 157310, 157330, 157370, 157390, 157490, 157610, 157670, 157730, 157870, 157910, 157970, 158030, 158090, 158170, 158230, 158590, 158770, 158810, 158870, 158890, 159010, 159070, 159130, 159190, 159230, 159370, 159590, 159710, 159730, 159910, 160010, 160070, 160330, 160570, 160610, 160630, 160670, 160690, 160730, 160870, 160910, 160970, 161030, 161110, 161270, 161390, 161410, 161830, 161870, 161890, 161930, 162170, 162230, 162290, 162310, 162490, 162530, 162670, 162730, 163010, 163190, 163330, 163390, 163490, 163610, 163630, 163690, 163810, 164110, 164170, 164210, 164270, 164330, 164470, 164510, 164530, 164770, 164810, 164870, 164930, 165190, 165290, 165470, 165530, 165610, 165670, 165730, 166030, 166070, 166190, 166310, 166330, 166490, 166510, 166570, 166610, 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---

 

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{1001690,100169}, {1001830,100183}, {1001890,100189}, {1001930,100193}, {1002070,100207}, {1002130,100213}, {1002370,100237}, {1002670,100267}, {1002710,100271}, {1002790,100279}, {1002910,100291}, {1002970,100297}, {1003130,100313}, {1003330,100333}, {1003430,100343}, {1003570,100357}, {1003610,100361}, {1003630,100363}, {1003790,100379}, {1003910,100391}, {1003930,100393}, {1004030,100403}, {1004110,100411}, {1004170,100417}, {1004470,100447}, {1004590,100459}, {1004690,100469}, {1004830,100483}, {1004930,100493}, {1005010,100501}, {1005110,100511}, {1005170,100517}, {1005190,100519}, {1005230,100523}, {1005370,100537}, {1005470,100547}, {1005490,100549}, {1005590,100559}, {1005910,100591}, {1006090,100609}, {1006130,100613}, {1006210,100621}, {1006490,100649}, {1006690,100669}, {1006730,100673}, {1006930,100693}, {1006990,100699}, {1007030,100703}, {1007330,100733}, {1007410,100741}, {1007470,100747}, {1007690,100769}, {1007870,100787}, {1007990,100799}, {1008010,100801}, {1008110,100811}, {1008230,100823}, {1008290,100829}, {1008470,100847}, {1008530,100853}, {1009070,100907}, {1009130,100913}, {1009270,100927}, {1009310,100931}, {1009370,100937}, {1009430,100943}, {1009570,100957}, {1009810,100981}, {1009870,100987}, {1009990,100999}, {1010090,101009}, {1010210,101021}, {1010270,101027}, {1010510,101051}, {1010630,101063}, {1010810,101081}, {1010890,101089}, {1011070,101107}, {1011110,101111}, {1011130,101113}, {1011170,101117}, {1011190,101119}, {1011410,101141}, {1011490,101149}, {1011590,101159}, {1011610,101161}, {1011730,101173}, {1011830,101183}, {1011970,101197}, {1012030,101203}, {1012070,101207}, {1012090,101209}, {1012210,101221}, {1012670,101267}, {1012730,101273}, {1012790,101279}, {1012810,101281}, {1012870,101287}, {1012930,101293}, {1013230,101323}, {1013330,101333}, {1013410,101341}, {1013470,101347}, {1013590,101359}, {1013630,101363}, {1013770,101377}, {1013830,101383}, {1013990,101399}, {1014110,101411}, {1014190,101419}, {1014290,101429}, {1014490,101449}, {1014670,101467}, {1014770,101477}, {1014830,101483}, {1014890,101489}, {1015010,101501}, {1015030,101503}, {1015130,101513}, {1015270,101527}, {1015310,101531}, {1015330,101533}, {1015370,101537}, {1015610,101561}, {1015730,101573}, {1015810,101581}, {1015990,101599}, {1016030,101603}, {1016110,101611}, {1016270,101627}, {1016410,101641}, {1016530,101653}, {1016630,101663}, {1016810,101681}, {1016930,101693}, {1017010,101701}, {1017190,101719}, {1017230,101723}, {1017370,101737}, {1017410,101741}, {1017470,101747}, {1017490,101749}, {1017710,101771}, {1017890,101789}, {1017970,101797}, {1018070,101807}, {1018330,101833}, {1018370,101837}, {1018390,101839}, {1018630,101863}, {1018690,101869}, {1018730,101873}, {1018790,101879}, {1018910,101891}, {1019170,101917}, {1019210,101921}, {1019290,101929}, {1019390,101939}, {1019570,101957}, {1019630,101963}, {1019770,101977}, {1019870,101987}, {1019990,101999}, {1020010,102001}, {1020130,102013}, {1020190,102019}, {1020230,102023}, {1020310,102031}, {1020430,102043}, {1020590,102059}, {1020610,102061}, {1020710,102071}, {1020770,102077}, {1020790,102079}, {1021010,102101}, {1021030,102103}, {1021070,102107}, {1021210,102121}, {1021390,102139}, {1021490,102149}, {1021610,102161}, {1021810,102181}, {1021910,102191}, {1021970,102197}, {1021990,102199}, {1022030,102203}, {1022170,102217}, {1022290,102229}, {1022330,102233}, {1022410,102241}, {1022510,102251}, {1022530,102253}, {1022590,102259}, {1022930,102293}, {1022990,102299}, {1023010,102301}, {1023170,102317}, {1023290,102329}, {1023370,102337}, {1023590,102359}, {1023670,102367}, {1023970,102397}, {1024070,102407}, {1024090,102409}, {1024330,102433}, {1024370,102437}, {1024510,102451}, {1024610,102461}, {1024810,102481}, {1024970,102497}, {1024990,102499}, {1025030,102503}, {1025230,102523}, {1025330,102533}, {1025390,102539}, {1025470,102547}, {1025510,102551}, {1025590,102559}, {1025630,102563}, {1025870,102587}, {1025930,102593}, {1026070,102607}, {1026110,102611}, {1026430,102643}, {1026470,102647}, {1026530,102653}, {1026670,102667}, {1026730,102673}, {1026770,102677}, {1026790,102679}, {1027010,102701}, {1027610,102761}, {1027630,102763}, {1027690,102769}, {1027930,102793}, {1027970,102797}, {1028110,102811}, {1028290,102829}, {1028410,102841}, {1028590,102859}, {1028710,102871}, {1028770,102877}, {1028810,102881}, {1029110,102911}, {1029130,102913}, {1029290,102929}, {1029310,102931}, {1029530,102953}, {1029670,102967}, {1029830,102983}, {1030010,103001}, {1030070,103007}, {1030430,103043}, {1030490,103049}, {1030670,103067}, {1030690,103069}, {1030790,103079}, {1030870,103087}, {1030910,103091}, {1030930,103093}, {1030990,103099}, {1031230,103123}, {1031410,103141}, {1031710,103171}, {1031770,103177}, {1031830,103183}, {1032170,103217}, {1032310,103231}, {1032370,103237}, {1032890,103289}, {1032910,103291}, {1033070,103307}, {1033190,103319}, {1033330,103333}, {1033490,103349}, {1033570,103357}, {1033870,103387}, {1033910,103391}, {1033930,103393}, {1033990,103399}, {1034090,103409}, {1034210,103421}, {1034230,103423}, {1034510,103451}, {1034570,103457}, {1034710,103471}, {1034830,103483}, {1035110,103511}, {1035290,103529}, {1035490,103549}, {1035530,103553}, {1035610,103561}, {1035670,103567}, {1035730,103573}, {1035770,103577}, {1035830,103583}, {1035910,103591}, {1036130,103613}, {1036190,103619}, {1036430,103643}, {1036510,103651}, {1036570,103657}, {1036690,103669}, {1036810,103681}, {1036870,103687}, {1036990,103699}, {1037030,103703}, {1037230,103723}, {1037690,103769}, {1037870,103787}, {1038010,103801}, {1038110,103811}, {1038130,103813}, {1038370,103837}, {1038410,103841}, {1038430,103843}, {1038670,103867}, {1038890,103889}, {1039030,103903}, {1039130,103913}, {1039190,103919}, {1039510,103951}, {1039630,103963}, {1039670,103967}, {1039690,103969}, {1039790,103979}, {1039810,103981}, {1039910,103991}, {1039930,103993}, {1039970,103997}, {1040030,104003}, {1040090,104009}, {1040210,104021}, {1040330,104033}, {1040470,104047}, {1040530,104053}, {1040590,104059}, {1040870,104087}, {1040890,104089}, {1041070,104107}, {1041130,104113}, {1041190,104119}, {1041230,104123}, {1041470,104147}, {1041490,104149}, {1041610,104161}, {1041730,104173}, {1041790,104179}, {1041830,104183}, {1042070,104207}, {1042310,104231}, {1042330,104233}, {1042390,104239}, {1042430,104243}, {1042810,104281}, {1042870,104287}, {1042970,104297}, {1043090,104309}, {1043110,104311}, {1043230,104323}, {1043270,104327}, {1043470,104347}, {1043690,104369}, {1043810,104381}, {1043830,104383}, {1043930,104393}, {1043990,104399}, {1044170,104417}, {1044590,104459}, {1044710,104471}, {1044730,104473}, {1044790,104479}, {1044910,104491}, {1045130,104513}, {1045270,104527}, {1045370,104537}, {1045430,104543}, {1045490,104549}, {1045510,104551}, {1045610,104561}, {1045790,104579}, {1045930,104593}, {1045970,104597}, {1046230,104623}, {1046390,104639}, {1046510,104651}, {1046590,104659}, {1046770,104677}, {1046810,104681}, {1046830,104683}, {1046930,104693}, {1047010,104701}, {1047070,104707}, {1047110,104711}, {1047170,104717}, {1047230,104723}, {1047290,104729}}

 

---

 

Liste des embêteurs ne finissant pas par 0 (embêteurs = embedders ;o)

 

{12, 35, 57, 447, 453, 459, 561, 567, 671, 779, 783, 789, 897, 1113, 1127, 1131, 1137, 1139, 1149, 2223, 2227, 2229, 2233, 3337, 4449, 7787, 7797, 7809, 7811, 7821, 8907, 8911, 8919, 22237, 22239, 22243, 22251, 22267, 22269, 44447, 44451, 44457, 44463, 44481, 55557, 55563, 55569, 55573, 55581, 55591, 55623, 66673, 66679, 66689, 66691, 77789, 77793, 77817, 77823, 77829, 77841, 77853, 88893, 88923, 88929, 88933, 88941, 111113, 111117, 222229, 333343, 333347, 555579, 777783, 777797, 777801, 777813, 888897, 888903, 1111119, 1111121, 1111127, 1111143, 1111149, 1111187, 1111191, 2222247, 2222269, 2222289, 3333337, 3333341, 3333349, 3333367}

 

La même liste assortie pour chacun de leur nombre premier accompagnateur :

 

{{12,2}, {35,5}, {57,7}, {447,47}, {453,53}, {459,59}, {561,61}, {567,67}, {671,71}, {779,79}, {783,83}, {789,89}, {897,97}, {1113,113}, {1127,127}, {1131,131}, {1137,137}, {1139,139}, {1149,149}, {2223,223}, {2227,227}, {2229,229}, {2233,233}, {3337,337}, {4449,449}, {7787,787}, {7797,797}, {7809,809}, {7811,811}, {7821,821}, {8907,907}, {8911,911}, {8919,919}, {22237,2237}, {22239,2239}, {22243,2243}, {22251,2251}, {22267,2267}, {22269,2269}, {44447,4447}, {44451,4451}, {44457,4457}, {44463,4463}, {44481,4481}, {55557,5557}, {55563,5563}, {55569,5569}, {55573,5573}, {55581,5581}, {55591,5591}, {55623,5623}, {66673,6673}, {66679,6679}, {66689,6689}, {66691,6691}, {77789,7789}, {77793,7793}, {77817,7817}, {77823,7823}, {77829,7829}, {77841,7841}, {77853,7853}, {88893,8893}, {88923,8923}, {88929,8929}, {88933,8933}, {88941,8941}, {111113,11113}, {111117,11117}, {222229,22229}, {333343,33343}, {333347,33347}, {555579,55579}, {777783,77783}, {777797,77797}, {777801,77801}, {777813,77813}, {888897,88897}, {888903,88903}, {1111119,111119}, {1111121,111121}, {1111127,111127}, {1111143,111143}, {1111149,111149}, {1111187,111187}, {1111191,111191}, {2222247,222247}, {2222269,222269}, {2222289,222289}, {3333337,333337}, {3333341,333341}, {3333349,333349}, {3333367,333367}}

 

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