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set of primes p whose p–1 give an Egyptian fraction for 1

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Dec 12th, 2019
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  1. {3, 7, 19, 23, 31, 37, 43, 47, 67, 79, 89, 103, 131, 137, 139, 191, 211, 239, 283, 419, 431, 443, 463, 547, 593, 647, 691, 859, 1033, 1039, 1069, 1103, 1129, 1237, 1871, 2029, 2293, 2347, 2383, 2393, 2539, 2557, 2647, 2741, 3041, 3079, 3187, 3307, 3323, 3371, 3373, 3547, 3709, 3733, 3853, 3911, 4567, 4931, 5227, 5347, 5351, 6343, 6421, 7411, 7537, 7937, 7951, 8221, 8753, 8779, 9011, 9049, 9187, 9277, 9341, 9397, 9437, 11779, 12101, 12547, 12821, 13009, 13121, 14341, 14407, 15149, 15271, 15919, 16057, 16087, 16573, 16699, 16987, 18133, 18521, 19231, 19237, 21157, 21569, 21977, 22003, 22091, 22549, 24517, 24851, 24971, 25849, 26647, 27581, 29717, 30259, 30341, 34297, 39877, 40013, 40627, 41549, 43691, 45433, 45737, 46153, 46279, 46301, 46451, 47797, 49999, 54559, 54727, 56737, 56993, 57773, 58693, 58937, 61949, 64663, 65111, 65899, 66373, 68729, 70537, 72031, 72911, 76597, 76831, 79589, 79669, 87751, 88397, 90617, 92857, 92893, 93811, 94219, 94291, 94889, 95707, 97579, 100291, 101839, 107687, 109639, 112291, 114649, 114671, 114679, 116741, 117577, 118033, 118717, 122599, 125141, 126761, 128389, 128683, 130769, 131059, 132367, 134731, 136177, 136541, 136769, 137209, 141307, 141619, 142421, 142981, 144037, 147629, 149551, 150061, 157571, 159521, 170707, 174487, 176419, 177917, 179461, 180221, 180289, 180379, 182779, 183499, 186859, 187631, 188491, 188869, 189671, 190471, 193247, 201589, 202381, 208721, 209359, 215503, 217369, 217577, 229693, 229699, 230137, 231017, 232751, 238331, 240967, 243161, 244471, 244529, 245029, 249187, 249199, 251621, 253387, 258197, 268969, 273613, 278051, 281777, 283601, 284743, 288049, 298211, 298343, 298631, 298999, 299419, 314779, 315109, 318701, 325093, 332803, 337543, 346589, 355363, 356749, 369191, 377263, 387577, 391453, 393247, 401057, 401161, 424343, 432449, 434923, 435641, 440443, 447319, 450103, 462713, 471259, 477409, 498403, 502141, 510137, 515941, 521539, 522637, 526717, 526741, 552707, 557611, 561091, 564163, 565517, 565727, 566173, 566737, 567883, 571069, 577177, 581149, 602983, 612331, 613451, 621317, 630871, 631717, 647659, 652153, 653749, 660067, 666089, 670457, 679951, 696991, 703949, 704419, 719833, 722539, 730757, 736387, 747497, 748849, 763937, 779869, 783569, 785053, 785753, 797201, 833309, 833537, 844631, 860393, 860891, 865807, 867371, 872057, 876311, 878467, 915049, 916291, 926111, 934481, 943289, 949777, 974107, 1008199, 1012217, 1018931, 1043743, 1055893, 1056361, 1070429, 1089799, 1093699, 1095439, 1102021, 1108909, 1108999, 1130651, 1133819, 1135427, 1139683, 1151611, 1152857, 1159339, 1161547, 1167209, 1172777, 1174171, 1181093, 1208561, 1213939, 1214333, 1234873, 1269253, 1287551, 1315837, 1349651, 1365289, 1368967, 1375937, 1377427, 1377931, 1401761, 1454003, 1466137, 1469357, 1470251, 1471409, 1479727, 1481071, 1486339, 1537661, 1559647, 1590551, 1600519, 1620769, 1649359, 1671521, 1680181, 1699457, 1713641, 1714931, 1729033, 1738727, 1754377, 1760287, 1766707, 1772971, 1795543, 1807231, 1874993, 1925057, 1934437, 2027323, 2058857, 2102171, 2126329, 2126809, 2138491, 2151137, 2151269, 2151319, 2163829, 2164901, 2171599, 2188031, 2221997, 2240723, 2248271, 2269027, 2275769, 2282477, 2291033, 2310029, 2312347, 2316151, 2342731, 2346277, 2353801, 2362571, 2378797, 2417743, 2419777, 2451811, 2462827, 2493187, 2527097, 2560357, 2576731, 2612893, 2667641, 2673739, 2683657, 2719141, 2762251, 2803441, 2919671, 2938073, 2964557, 3040003, 3067297, 3107633, 3115633, 3134057, 3141643, 3193097, 3248731, 3249061, 3261967, 3290051, 3332869, 3356741, 3413227, 3422569, 3436357, 3460397, 3471343, 3475489, 3503039, 3505477, 3513761, 3518329, 3571741, 3626291, 3670171, 3683021, 3690871, 3725207, 3943193, 3956671, 4043539, 4043771, 4067071, 4224377, 4278077, 4289927, 4311607, 4334417, 4334989, 4339817, 4385971, 4466989, 4483363, 4589561, 4593221, 4609531, 4634527, 4678783, 4687217, 4798309, 4814449, 4894093, 4908451, 4955627, 4963253, 5041937, 5077889, 5167807, 5224991, 5263253, 5292857, 5320327, 5327017, 5329397, 5368999, 5370353, 5398543, 5399351, 5400793, 5408653, 5413937, 5465149, 5496247, 5507471, 5572097, 5580581, 5580769, 5621179, 5777593, 5788357, 5885897, 5910313, 5920549, 5929853, 6001157, 6022507, 6134533, 6152621, 6165217, 6200503, 6262453, 6327473, 6455017, 6478033, 6547129, 6574357, 6592783, 6672467, 6697189, 6729517, 6779497, 6803201, 6835061, 6840583, 6841951, 6901087, 6912517, 7014691, 7028299, 7053493, 7097809, 7112351, 7218049, 7268213, 7292407, 7297421, 7308013, 7308019, 7349369, 7457929, 7508191, 7509233, 7565633, 7634443, 7642577, 7690967, 7849579, 7926041, 7947553, 7988093, 8058733, 8109061, 8181079, 8201377, 8247713, 8283559, 8353529, 8448763, 8588473, 8626841, 8640409, 8640601, 8763773, 8766517, 8794381, 8887631, 8898937, 8960729, 9043093, 9055181, 9099737, 9122741, 9125203, 9130841, 9132619, 9142577, 9149419, 9165347, 9169063, 9226531, 9250337, 9264209, 9276191, 9279953, 9461657, 9603457, 9604193, 9627109, 9763231, 9767591, 9974827, 10059613, 10095577, 10109789, 10140017, 10140943, 10396549, 10493569, 10650727, 10764973, 10813189, 10818637, 10823171, 10840259, 11195677, 11252677, 11278691, 11481157, 11481317, 11515631, 11567669, 11934281, 12096439, 12106361, 12107057, 12149971, 12193429, 12428321, 12630391, 12875917, 12927451, 12939163, 12969403, 13278611, 13286417, 13353667, 13417577, 13424491, 13508377, 13556381, 13755509, 13766713, 13937351, 13988537, 14057713, 14239361, 14308807, 14327897, 14546569, 14609737, 14732461, 14880871, 15139417, 15139457, 15435617, 15498521, 15555877, 15570251, 15768551, 15859757, 15868603, 15884527, 15929789, 16034713, 16102969, 16104289, 16168469, 16297357, 16334953, 16338137, 16360837, 16429297, 16429379, 16429519, 16429687, 16495411, 16552841, 16554017, 16555481, 16664897, 16672417, 16698007, 16764529, 16835597, 16842149, 16859287, 16876547, 16882039, 16917749, 17179901, 17310157, 17425313, 17626787, 17906237, 17994997, 18029897, 18031451, 18038143, 18072449, 18467093, 18555643, 18611297, 18678889, 18898931, 18903307, 18941777, 18950297, 18996727, 19007077, 19157617, 19208489, 19292993, 19320877, 19505471, 19518211, 19578127, 19590913, 19676179, 19677181, 19760599, 19939457, 19953379, 20007601, 20016523, 20040829, 20277239, 20518577, 20520221, 20940449, 21156257, 21291671, 21595241, 22085311, 22162687, 22163683, 22265981, 22368079, 22431733, 22668091, 22779791, 22875709, 23030297, 23202169, 23268881, 23443361, 23625013, 24461537, 24635899, 24694937, 24999529, 25300003, 25445951, 25534447, 25633457, 25767481, 26275721, 26313247, 26460011, 26496859, 26497277, 26594219, 26631757, 26939657, 26959721, 27147209, 27194569, 27300787, 27310693, 27372337, 27510061, 27511331, 27525791, 27588851, 28013407, 28056439, 28192807, 28528537, 28622261, 28684727, 28692457, 28777937, 28779329, 28932931, 29002399, 29018261, 29078293, 29133829, 29506303, 29623513, 29858467, 30266503, 30620041, 30640087, 30708739, 30777793, 30827359, 30837061, 31079569, 31088023, 31341851, 31395317, 31426903, 31431013, 31439299, 31447253, 31596797, 31650823, 31699807, 31955557, 31988081, 32016931, 32362327, 32897209, 33111581, 33764077, 33771137, 33818237, 33840907, 34153531, 34365371, 34424417, 34574653, 34620169, 34622633, 35103307, 35560661, 35564413, 36138071, 36891307, 37064023, 37279399, 37547947, 37897901, 38087317, 38295869, 38301161, 38419933, 38786227, 38885471, 38885773, 39013537, 39375851, 39661841, 40253201, 40502591, 40545157, 40810751, 41324417, 41355557, 42004901, 42154873, 42190903, 42261397, 43557461, 43833221, 44177351, 44799463, 44920327, 44921537, 45448661, 45775151, 45862417, 45955297, 46022411, 46081459, 46572359, 46695533, 46756499, 46884169, 46928317, 47083583, 48215623, 48500693, 48889187, 49332131, 49521811, 49548403, 50218183, 50244463, 50406641, 50546273, 50864111, 51003559, 51044647, 51340777, 51434059, 51759817, 52103297, 52161299, 52977499, 53420009, 53551073, 53558773, 53566937, 53626841, 53731493, 54198037, 54371021, 54615919, 54682783, 54854557, 54854923, 55142497, 55260811, 55572493, 56502689, 56774153, 57211991, 57215407, 57572153, 57819319, 57919891, 57980071, 59174177, 59598937, 59743241, 60407117, 60608269, 61068169, 61504939, 61714027, 63562871, 63840013, 64231333, 65160943, 65251577, 66369739, 66370517, 66425057, 67716511, 68131997, 68854717, 68966017, 69189097, 70842557, 71504947, 71842807, 71842919, 71871511, 72007213, 72832729, 73144867, 73327853, 73329127, 75778621, 76715497, 76956931, 77022823, 78161357, 79392727, 79657609, 80019053, 80020477, 80660269, 82066219, 82730363, 83010079, 83417447, 83445913, 85472539, 85863007, 86460763, 86773657, 86907049, 87003151, 87920351, 88935877, 89264647, 89545123, 89847613, 90114823, 90699703, 90755737, 91802723, 92300569, 92524219, 92664287, 93306223, 93322171, 93395717, 93462953, 93759571, 94708697, 94856309, 95571911, 96992767, 97013821, 97079867, 97683379, 98256863, 99911051, 100298851, 101513557, 101699509, 102095593, 102633151, 103583509, 103593649, 104029663, 104791801, 105410849, 105661351, 105665737, 106579633, 106923823, 107540821, 107606011, 107959889, 109826729, 109831927, 109833551, 110314319, 110764337, 111113389, 111228043, 111234073, 111639313, 112505017, 113053561, 113079907, 113361901, 113524451, 113652353, 114255247, 114647977, 115410017, 115470317, 115647187, 115763833, 116389993, 116617363, 117677741, 117790193, 117931061, 118310041, 118428259, 118432289, 118437439, 118673173, 118934479, 118937317, 118982543, 121392199, 122046433, 122079341, 122960701, 124694029, 125421847, 126279481, 127729757, 127818697, 128015183, 128610877, 128795057, 128982439, 129365917, 131283727, 131553593, 132549217, 132580817, 132708943, 134304941, 135073661, 135150331, 135150451, 135206941, 136713481, 137919497, 138925541, 139069747, 139360327, 140326481, 140332931, 140731531, 140790371, 141670601, 144469057, 144868687, 145223569, 145433441, 145592351, 148277737, 148727737, 148803029, 149310929, 149318551, 149759633, 150374317, 150424411, 151077067, 153187297, 153743059, 153746741, 153834463, 155223127, 155387033, 155885497, 156895273, 157165649, 157193977, 157917953, 158452829, 159364873, 159627007, 159750739, 160759999, 162434383, 163533341, 163964051, 164075141, 164157859, 164524357, 165235687, 165311119, 165553097, 168638413, 171756509, 171756707, 172424177, 172686013, 173100233, 174399679, 174693143, 175755553, 177822191, 178062541, 178907957, 179221453, 179889013, 181920463, 182217023, 183662201, 183812437, 185693203, 186426557, 186538507, 187520779, 188118347, 188123113, 188249417, 190550303, 191745551, 192008683, 192489611, 192836929, 193391741, 196211377, 196507099, 197158111, 197345143, 197587037, 197976487, 198180791, 198447407, 198866411, 198867041, 198989801, 201353261, 203884189, 204416369, 205037491, 205212391, 205234327, 205345807, 205422671, 205494607, 205511029, 206609329, 209123773, 214943587, 214996849, 215767787, 217032181, 220701697, 222610657, 224424619, 225300937, 226080919, 227795353, 228244337, 228874901, 229195937, 229529491, 229732823, 230488337, 230555851, 231141907, 231378977, 236200903, 237562277, 238241389, 239148379, 239599433, 239625797, 240104119, 241180117, 241186793, 244137701, 245579563, 245739961, 246113183, 246132847, 246191509, 247153789, 248571199, 248648417, 250141471, 251519977, 251702149, 251997857, 252143453, 252940003, 253456193, 256734043, 258727639, 261380827, 262323797, 262964707, 263045897, 263048239, 263671841, 264218341, 264954971, 265853611, 266037529, 266379163, 266486291, 268047713, 269721377, 269819153, 270304939, 271113301, 271504663, 274270961, 275795911, 277914899, 279172207, 279983801, 281786387, 282178433, 282683059, 283023617, 286322437, 286322447, 288576857, 289783591, 290032123, 291716653, 294394561, 295515739, 298484701, 298865971, 300420187, 300553777, 300799043, 302918857, 303411557, 305257241, 305461237, 306623689, 306729389, 307606207, 308744971, 309969701, 311594417, 312019049, 313682311, 314370997, 314966441, 315441547, 324827171, 325933241, 328378073, 332620601, 333925297, 333941057, 336037519, 337132063, 344348887, 347450863, 350825609, 351130837, 352192901, 353337629, 354015829, 354300491, 357128341, 363043537, 363219319, 366628897, 369471227, 369982693, 370228361, 371387563, 376681271, 376933021, 378833479, 379818701, 382657237, 386879293, 387792193, 388006093, 391375351, 392014471, 393047653, 394814027, 395924861, 397160473, 397287427, 400073227, 400425617, 402085393, 402178181, 402980311, 404449069, 405120559, 405804967, 408072901, 408906637, 416323447, 417759739, 419101219, 419841361, 422438339, 423057277, 423536741, 423866851, 427987537, 429990937, 431106601, 431187461, 431483419, 432521237, 435245731, 435767209, 438084727, 438170287, 440793037, 445419019, 446521511, 458203111, 459235961, 461387951, 463785701, 465727957, 465942881, 467681341, 469105211, 469930039, 472702253, 474337933, 477409489, 477612211, 478655293, 478900327, 481830449, 484152491, 484595479, 484740031, 485471989, 485501959, 486828101, 488298401, 494815901, 495596653, 497083427, 499101193, 500409563, 500504677, 502179889, 502999891, 507088537, 509355563, 509466791, 509737853, 512183921, 514163131, 515045449, 515482531, 519383191, 519577897, 521608097, 522074359, 522807067, 523607237, 527747111, 528417821, 528450319, 528916153, 529603441, 530210273, 531591611, 532050263, 534524923, 535212169, 536251327, 536351017, 538332569, 538572247, 545443207, 545716207, 547173437, 547207057, 547322311, 547952239, 548265469, 548837291, 552230647, 552797813, 556045573, 556170361, 557054261, 559614491, 560934551, 563124589, 568095397, 577679273, 578199163, 580826563, 581669261, 581789893, 585657427, 587287601, 588285301, 590935157, 595603909, 601160951, 601161073, 603216221, 608218453, 613481887, 614049691, 614162711, 617929513, 620318767, 625024717, 626614057, 628885057, 629237821, 630594499, 630745057, 631839431, 635831761, 636408709, 644291371, 644406589, 645181751, 647217817, 647740589, 649837063, 650453801, 654678931, 656837009, 660179563, 661656623, 663817541, 666018943, 666259171, 668231569, 668445377, 669486863, 669552971, 672987373, 675424741, 680479427, 683353969, 686916847, 686939831, 689237677, 689614771, 692544607, 696128617, 696154397, 698106389, 704418731, 705764369, 714247459, 715440871, 717247523, 717693887, 717951809, 730268047, 731724457, 734020997, 735083201, 739726313, 741549077, 742415801, 745357471, 745837459, 747526537, 749642689, 752262149, 754067189, 756245669, 756257977, 760156841, 765446083, 768863009, 772321687, 773973839, 775344553, 779918959, 781842547, 787311257, 788864569, 790667057, 791147171, 801138367, 804926711, 806693539, 811633217, 812252293, 820065217, 820939753, 825089053, 829844419, 835700659, 839980117, 840792149, 841473487, 842654411, 843155021, 851880797, 854316109, 856814533, 858676807, 862492109, 864103309, 866077321, 867402911, 868255147, 868988597, 870611771, 873062227, 876117439, 876537047, 876718603, 878894311, 882364289, 884871671, 886977097, 888903649, 892434143, 892511791, 894766507, 896512987, 899936899, 905063989, 906260741, 910511443, 910718863, 919513409, 924358469, 929431969, 930357803, 931612879, 935883653, 937267399, 942497191, 944086331, 944898991, 946742119, 949311931, 952819081, 953111321, 954102433, 956158267, 972815957, 974180657, 979729831, 984229837, 991967803, 1004611897, 1007241941, 1011530587, 1014739987, 1015380787, 1015695851, 1016371649, 1026181603, 1026744151, 1033924417, 1034199997, 1042555123, 1050229387, 1055985893, 1060133689, 1064219353, 1077697477, 1078326163, 1080276107, 1082597653, 1086855793, 1094092897, 1098453637, 1098593257, 1100310109, 1104494779, 1106174899, 1108707631, 1116643511, 1122894977, 1124612791, 1125071209, 1152065921, 1153014211, 1156179097, 1160545777, 1162025317, 1162081651, 1166121311, 1168217597, 1168956757, 1169437627, 1171847141, 1173410323, 1177887911, 1179018871, 1182259063, 1189130051, 1198037287, 1201545281, 1203784531, 1207258721, 1212929981, 1217847913, 1223084201, 1236474553, 1238155403, 1240124141, 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