yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
365537	365537	[ "365537 365537 1" ]
3448761	3 1149587	[ "3448761 3 1149587", "1149587 1149587 1" ]
3947598	2 3 3 219311	[ "3947598 2 1973799", "1973799 3 657933", "657933 3 219311", "219311 219311 1" ]
3514327	1571 2237	[ "3514327 1571 2237", "2237 2237 1" ]
2898535	5 579707	[ "2898535 5 579707", "579707 579707 1" ]
3212592	2 2 2 2 3 17 31 127	[ "3212592 2 1606296", "1606296 2 803148", "803148 2 401574", "401574 2 200787", "200787 3 66929", "66929 17 3937", "3937 31 127", "127 127 1" ]
3053173	3053173	[ "3053173 3053173 1" ]
2527369	13 194413	[ "2527369 13 194413", "194413 194413 1" ]
792501	3 264167	[ "792501 3 264167", "264167 264167 1" ]
4355372	2 2 7 23 6763	[ "4355372 2 2177686", "2177686 2 1088843", "1088843 7 155549", "155549 23 6763", "6763 6763 1" ]
2259668	2 2 564917	[ "2259668 2 1129834", "1129834 2 564917", "564917 564917 1" ]
3874585	5 11 13 5419	[ "3874585 5 774917", "774917 11 70447", "70447 13 5419", "5419 5419 1" ]
2947079	101 29179	[ "2947079 101 29179", "29179 29179 1" ]
2090395	5 418079	[ "2090395 5 418079", "418079 418079 1" ]
1513918	2 7 17 6361	[ "1513918 2 756959", "756959 7 108137", "108137 17 6361", "6361 6361 1" ]
4576934	2 2288467	[ "4576934 2 2288467", "2288467 2288467 1" ]
2687199	3 37 43 563	[ "2687199 3 895733", "895733 37 24209", "24209 43 563", "563 563 1" ]
3632509	17 157 1361	[ "3632509 17 213677", "213677 157 1361", "1361 1361 1" ]
2997858	2 3 19 26297	[ "2997858 2 1498929", "1498929 3 499643", "499643 19 26297", "26297 26297 1" ]
1326068	2 2 17 19501	[ "1326068 2 663034", "663034 2 331517", "331517 17 19501", "19501 19501 1" ]
4347558	2 3 3 41 43 137	[ "4347558 2 2173779", "2173779 3 724593", "724593 3 241531", "241531 41 5891", "5891 43 137", "137 137 1" ]
2586659	2586659	[ "2586659 2586659 1" ]
1844635	5 13 13 37 59	[ "1844635 5 368927", "368927 13 28379", "28379 13 2183", "2183 37 59", "59 59 1" ]
2906257	23 126359	[ "2906257 23 126359", "126359 126359 1" ]
2813153	7 23 101 173	[ "2813153 7 401879", "401879 23 17473", "17473 101 173", "173 173 1" ]
3786292	2 2 946573	[ "3786292 2 1893146", "1893146 2 946573", "946573 946573 1" ]
2176855	5 435371	[ "2176855 5 435371", "435371 435371 1" ]
3525528	2 2 2 3 17 8641	[ "3525528 2 1762764", "1762764 2 881382", "881382 2 440691", "440691 3 146897", "146897 17 8641", "8641 8641 1" ]
127628	2 2 31907	[ "127628 2 63814", "63814 2 31907", "31907 31907 1" ]
429681	3 7 7 37 79	[ "429681 3 143227", "143227 7 20461", "20461 7 2923", "2923 37 79", "79 79 1" ]
1300618	2 11 59119	[ "1300618 2 650309", "650309 11 59119", "59119 59119 1" ]
95198	2 47599	[ "95198 2 47599", "47599 47599 1" ]
1840732	2 2 137 3359	[ "1840732 2 920366", "920366 2 460183", "460183 137 3359", "3359 3359 1" ]
2053094	2 1026547	[ "2053094 2 1026547", "1026547 1026547 1" ]
2925652	2 2 731413	[ "2925652 2 1462826", "1462826 2 731413", "731413 731413 1" ]
2953930	2 5 7 19 2221	[ "2953930 2 1476965", "1476965 5 295393", "295393 7 42199", "42199 19 2221", "2221 2221 1" ]
59025	3 5 5 787	[ "59025 3 19675", "19675 5 3935", "3935 5 787", "787 787 1" ]
1009897	7 144271	[ "1009897 7 144271", "144271 144271 1" ]
1562999	1562999	[ "1562999 1562999 1" ]
1089588	2 2 3 29 31 101	[ "1089588 2 544794", "544794 2 272397", "272397 3 90799", "90799 29 3131", "3131 31 101", "101 101 1" ]
2300280	2 2 2 3 5 29 661	[ "2300280 2 1150140", "1150140 2 575070", "575070 2 287535", "287535 3 95845", "95845 5 19169", "19169 29 661", "661 661 1" ]
1988633	1988633	[ "1988633 1988633 1" ]
751970	2 5 29 2593	[ "751970 2 375985", "375985 5 75197", "75197 29 2593", "2593 2593 1" ]
3331647	3 3 11 73 461	[ "3331647 3 1110549", "1110549 3 370183", "370183 11 33653", "33653 73 461", "461 461 1" ]
4830473	53 91141	[ "4830473 53 91141", "91141 91141 1" ]
3589164	2 2 3 3 3 167 199	[ "3589164 2 1794582", "1794582 2 897291", "897291 3 299097", "299097 3 99699", "99699 3 33233", "33233 167 199", "199 199 1" ]
2502768	2 2 2 2 3 23 2267	[ "2502768 2 1251384", "1251384 2 625692", "625692 2 312846", "312846 2 156423", "156423 3 52141", "52141 23 2267", "2267 2267 1" ]
2024125	5 5 5 16193	[ "2024125 5 404825", "404825 5 80965", "80965 5 16193", "16193 16193 1" ]
3830502	2 3 13 49109	[ "3830502 2 1915251", "1915251 3 638417", "638417 13 49109", "49109 49109 1" ]
3755395	5 7 41 2617	[ "3755395 5 751079", "751079 7 107297", "107297 41 2617", "2617 2617 1" ]
862196	2 2 439 491	[ "862196 2 431098", "431098 2 215549", "215549 439 491", "491 491 1" ]
4185199	103 179 227	[ "4185199 103 40633", "40633 179 227", "227 227 1" ]
1126499	11 102409	[ "1126499 11 102409", "102409 102409 1" ]
765021	3 255007	[ "765021 3 255007", "255007 255007 1" ]
3211881	3 23 46549	[ "3211881 3 1070627", "1070627 23 46549", "46549 46549 1" ]
105070	2 5 7 19 79	[ "105070 2 52535", "52535 5 10507", "10507 7 1501", "1501 19 79", "79 79 1" ]
1777286	2 7 126949	[ "1777286 2 888643", "888643 7 126949", "126949 126949 1" ]
2894227	7 413461	[ "2894227 7 413461", "413461 413461 1" ]
1151401	1151401	[ "1151401 1151401 1" ]
4463242	2 7 23 83 167	[ "4463242 2 2231621", "2231621 7 318803", "318803 23 13861", "13861 83 167", "167 167 1" ]
4095232	2 2 2 2 2 2 2 2 17 941	[ "4095232 2 2047616", "2047616 2 1023808", "1023808 2 511904", "511904 2 255952", "255952 2 127976", "127976 2 63988", "63988 2 31994", "31994 2 15997", "15997 17 941", "941 941 1" ]
2552506	2 11 157 739	[ "2552506 2 1276253", "1276253 11 116023", "116023 157 739", "739 739 1" ]
855510	2 3 5 28517	[ "855510 2 427755", "427755 3 142585", "142585 5 28517", "28517 28517 1" ]
1324405	5 264881	[ "1324405 5 264881", "264881 264881 1" ]
4559969	4559969	[ "4559969 4559969 1" ]
3537367	157 22531	[ "3537367 157 22531", "22531 22531 1" ]
1245689	1245689	[ "1245689 1245689 1" ]
838339	47 17837	[ "838339 47 17837", "17837 17837 1" ]
1107929	1107929	[ "1107929 1107929 1" ]
3652236	2 2 3 3 3 7 4831	[ "3652236 2 1826118", "1826118 2 913059", "913059 3 304353", "304353 3 101451", "101451 3 33817", "33817 7 4831", "4831 4831 1" ]
3633747	3 13 23 4051	[ "3633747 3 1211249", "1211249 13 93173", "93173 23 4051", "4051 4051 1" ]
1371300	2 2 3 5 5 7 653	[ "1371300 2 685650", "685650 2 342825", "342825 3 114275", "114275 5 22855", "22855 5 4571", "4571 7 653", "653 653 1" ]
1952310	2 3 5 59 1103	[ "1952310 2 976155", "976155 3 325385", "325385 5 65077", "65077 59 1103", "1103 1103 1" ]
2399310	2 3 3 5 53 503	[ "2399310 2 1199655", "1199655 3 399885", "399885 3 133295", "133295 5 26659", "26659 53 503", "503 503 1" ]
4278986	2 2139493	[ "4278986 2 2139493", "2139493 2139493 1" ]
3992574	2 3 665429	[ "3992574 2 1996287", "1996287 3 665429", "665429 665429 1" ]
4199317	23 182579	[ "4199317 23 182579", "182579 182579 1" ]
3263351	7 7 13 47 109	[ "3263351 7 466193", "466193 7 66599", "66599 13 5123", "5123 47 109", "109 109 1" ]
2248248	2 2 2 3 113 829	[ "2248248 2 1124124", "1124124 2 562062", "562062 2 281031", "281031 3 93677", "93677 113 829", "829 829 1" ]
2734242	2 3 7 65101	[ "2734242 2 1367121", "1367121 3 455707", "455707 7 65101", "65101 65101 1" ]
240243	3 73 1097	[ "240243 3 80081", "80081 73 1097", "1097 1097 1" ]
2395201	79 30319	[ "2395201 79 30319", "30319 30319 1" ]
131408	2 2 2 2 43 191	[ "131408 2 65704", "65704 2 32852", "32852 2 16426", "16426 2 8213", "8213 43 191", "191 191 1" ]
4590007	4590007	[ "4590007 4590007 1" ]
376705	5 7 47 229	[ "376705 5 75341", "75341 7 10763", "10763 47 229", "229 229 1" ]
2987709	3 995903	[ "2987709 3 995903", "995903 995903 1" ]
287592	2 2 2 3 23 521	[ "287592 2 143796", "143796 2 71898", "71898 2 35949", "35949 3 11983", "11983 23 521", "521 521 1" ]
1268494	2 634247	[ "1268494 2 634247", "634247 634247 1" ]
856431	3 3 43 2213	[ "856431 3 285477", "285477 3 95159", "95159 43 2213", "2213 2213 1" ]
3662014	2 23 79609	[ "3662014 2 1831007", "1831007 23 79609", "79609 79609 1" ]
4011675	3 5 5 89 601	[ "4011675 3 1337225", "1337225 5 267445", "267445 5 53489", "53489 89 601", "601 601 1" ]
4424396	2 2 1106099	[ "4424396 2 2212198", "2212198 2 1106099", "1106099 1106099 1" ]
2964263	23 359 359	[ "2964263 23 128881", "128881 359 359", "359 359 1" ]
2980751	317 9403	[ "2980751 317 9403", "9403 9403 1" ]
1125160	2 2 2 5 23 1223	[ "1125160 2 562580", "562580 2 281290", "281290 2 140645", "140645 5 28129", "28129 23 1223", "1223 1223 1" ]
1934776	2 2 2 241847	[ "1934776 2 967388", "967388 2 483694", "483694 2 241847", "241847 241847 1" ]
3250927	17 191231	[ "3250927 17 191231", "191231 191231 1" ]
3957523	83 47681	[ "3957523 83 47681", "47681 47681 1" ]
2805889	131 21419	[ "2805889 131 21419", "21419 21419 1" ]
3994184	2 2 2 17 43 683	[ "3994184 2 1997092", "1997092 2 998546", "998546 2 499273", "499273 17 29369", "29369 43 683", "683 683 1" ]

365537

[ "365537 365537 1" ]

3448761

3 1149587

[ "3448761 3 1149587", "1149587 1149587 1" ]

3947598

2 3 3 219311

[ "3947598 2 1973799", "1973799 3 657933", "657933 3 219311", "219311 219311 1" ]

3514327

1571 2237

[ "3514327 1571 2237", "2237 2237 1" ]

2898535

5 579707

[ "2898535 5 579707", "579707 579707 1" ]

3212592

2 2 2 2 3 17 31 127

[ "3212592 2 1606296", "1606296 2 803148", "803148 2 401574", "401574 2 200787", "200787 3 66929", "66929 17 3937", "3937 31 127", "127 127 1" ]

3053173

[ "3053173 3053173 1" ]

2527369

13 194413

[ "2527369 13 194413", "194413 194413 1" ]

792501

3 264167

[ "792501 3 264167", "264167 264167 1" ]

4355372

2 2 7 23 6763

[ "4355372 2 2177686", "2177686 2 1088843", "1088843 7 155549", "155549 23 6763", "6763 6763 1" ]

2259668

2 2 564917

[ "2259668 2 1129834", "1129834 2 564917", "564917 564917 1" ]

3874585

5 11 13 5419

[ "3874585 5 774917", "774917 11 70447", "70447 13 5419", "5419 5419 1" ]

2947079

101 29179

[ "2947079 101 29179", "29179 29179 1" ]

2090395

5 418079

[ "2090395 5 418079", "418079 418079 1" ]

1513918

2 7 17 6361

[ "1513918 2 756959", "756959 7 108137", "108137 17 6361", "6361 6361 1" ]

4576934

2 2288467

[ "4576934 2 2288467", "2288467 2288467 1" ]

2687199

3 37 43 563

[ "2687199 3 895733", "895733 37 24209", "24209 43 563", "563 563 1" ]

3632509

17 157 1361

[ "3632509 17 213677", "213677 157 1361", "1361 1361 1" ]

2997858

2 3 19 26297

[ "2997858 2 1498929", "1498929 3 499643", "499643 19 26297", "26297 26297 1" ]

1326068

2 2 17 19501

[ "1326068 2 663034", "663034 2 331517", "331517 17 19501", "19501 19501 1" ]

4347558

2 3 3 41 43 137

[ "4347558 2 2173779", "2173779 3 724593", "724593 3 241531", "241531 41 5891", "5891 43 137", "137 137 1" ]

2586659

[ "2586659 2586659 1" ]

1844635

5 13 13 37 59

[ "1844635 5 368927", "368927 13 28379", "28379 13 2183", "2183 37 59", "59 59 1" ]

2906257

23 126359

[ "2906257 23 126359", "126359 126359 1" ]

2813153

7 23 101 173

[ "2813153 7 401879", "401879 23 17473", "17473 101 173", "173 173 1" ]

3786292

2 2 946573

[ "3786292 2 1893146", "1893146 2 946573", "946573 946573 1" ]

2176855

5 435371

[ "2176855 5 435371", "435371 435371 1" ]

3525528

2 2 2 3 17 8641

[ "3525528 2 1762764", "1762764 2 881382", "881382 2 440691", "440691 3 146897", "146897 17 8641", "8641 8641 1" ]

127628

2 2 31907

[ "127628 2 63814", "63814 2 31907", "31907 31907 1" ]

429681

3 7 7 37 79

[ "429681 3 143227", "143227 7 20461", "20461 7 2923", "2923 37 79", "79 79 1" ]

1300618

2 11 59119

[ "1300618 2 650309", "650309 11 59119", "59119 59119 1" ]

95198

2 47599

[ "95198 2 47599", "47599 47599 1" ]

1840732

2 2 137 3359

[ "1840732 2 920366", "920366 2 460183", "460183 137 3359", "3359 3359 1" ]

2053094

2 1026547

[ "2053094 2 1026547", "1026547 1026547 1" ]

2925652

2 2 731413

[ "2925652 2 1462826", "1462826 2 731413", "731413 731413 1" ]

2953930

2 5 7 19 2221

[ "2953930 2 1476965", "1476965 5 295393", "295393 7 42199", "42199 19 2221", "2221 2221 1" ]

59025

3 5 5 787

[ "59025 3 19675", "19675 5 3935", "3935 5 787", "787 787 1" ]

1009897

7 144271

[ "1009897 7 144271", "144271 144271 1" ]

1562999

[ "1562999 1562999 1" ]

1089588

2 2 3 29 31 101

[ "1089588 2 544794", "544794 2 272397", "272397 3 90799", "90799 29 3131", "3131 31 101", "101 101 1" ]

2300280

2 2 2 3 5 29 661

[ "2300280 2 1150140", "1150140 2 575070", "575070 2 287535", "287535 3 95845", "95845 5 19169", "19169 29 661", "661 661 1" ]

1988633

[ "1988633 1988633 1" ]

751970

2 5 29 2593

[ "751970 2 375985", "375985 5 75197", "75197 29 2593", "2593 2593 1" ]

3331647

3 3 11 73 461

[ "3331647 3 1110549", "1110549 3 370183", "370183 11 33653", "33653 73 461", "461 461 1" ]

4830473

53 91141

[ "4830473 53 91141", "91141 91141 1" ]

3589164

2 2 3 3 3 167 199

[ "3589164 2 1794582", "1794582 2 897291", "897291 3 299097", "299097 3 99699", "99699 3 33233", "33233 167 199", "199 199 1" ]

2502768

2 2 2 2 3 23 2267

[ "2502768 2 1251384", "1251384 2 625692", "625692 2 312846", "312846 2 156423", "156423 3 52141", "52141 23 2267", "2267 2267 1" ]

2024125

5 5 5 16193

[ "2024125 5 404825", "404825 5 80965", "80965 5 16193", "16193 16193 1" ]

3830502

2 3 13 49109

[ "3830502 2 1915251", "1915251 3 638417", "638417 13 49109", "49109 49109 1" ]

3755395

5 7 41 2617

[ "3755395 5 751079", "751079 7 107297", "107297 41 2617", "2617 2617 1" ]

862196

2 2 439 491

[ "862196 2 431098", "431098 2 215549", "215549 439 491", "491 491 1" ]

4185199

103 179 227

[ "4185199 103 40633", "40633 179 227", "227 227 1" ]

1126499

11 102409

[ "1126499 11 102409", "102409 102409 1" ]

765021

3 255007

[ "765021 3 255007", "255007 255007 1" ]

3211881

3 23 46549

[ "3211881 3 1070627", "1070627 23 46549", "46549 46549 1" ]

105070

2 5 7 19 79

[ "105070 2 52535", "52535 5 10507", "10507 7 1501", "1501 19 79", "79 79 1" ]

1777286

2 7 126949

[ "1777286 2 888643", "888643 7 126949", "126949 126949 1" ]

2894227

7 413461

[ "2894227 7 413461", "413461 413461 1" ]

1151401

[ "1151401 1151401 1" ]

4463242

2 7 23 83 167

[ "4463242 2 2231621", "2231621 7 318803", "318803 23 13861", "13861 83 167", "167 167 1" ]

4095232

2 2 2 2 2 2 2 2 17 941

[ "4095232 2 2047616", "2047616 2 1023808", "1023808 2 511904", "511904 2 255952", "255952 2 127976", "127976 2 63988", "63988 2 31994", "31994 2 15997", "15997 17 941", "941 941 1" ]

2552506

2 11 157 739

[ "2552506 2 1276253", "1276253 11 116023", "116023 157 739", "739 739 1" ]

855510

2 3 5 28517

[ "855510 2 427755", "427755 3 142585", "142585 5 28517", "28517 28517 1" ]

1324405

5 264881

[ "1324405 5 264881", "264881 264881 1" ]

4559969

[ "4559969 4559969 1" ]

3537367

157 22531

[ "3537367 157 22531", "22531 22531 1" ]

1245689

[ "1245689 1245689 1" ]

838339

47 17837

[ "838339 47 17837", "17837 17837 1" ]

1107929

[ "1107929 1107929 1" ]

3652236

2 2 3 3 3 7 4831

[ "3652236 2 1826118", "1826118 2 913059", "913059 3 304353", "304353 3 101451", "101451 3 33817", "33817 7 4831", "4831 4831 1" ]

3633747

3 13 23 4051

[ "3633747 3 1211249", "1211249 13 93173", "93173 23 4051", "4051 4051 1" ]

1371300

2 2 3 5 5 7 653

[ "1371300 2 685650", "685650 2 342825", "342825 3 114275", "114275 5 22855", "22855 5 4571", "4571 7 653", "653 653 1" ]

1952310

2 3 5 59 1103

[ "1952310 2 976155", "976155 3 325385", "325385 5 65077", "65077 59 1103", "1103 1103 1" ]

2399310

2 3 3 5 53 503

[ "2399310 2 1199655", "1199655 3 399885", "399885 3 133295", "133295 5 26659", "26659 53 503", "503 503 1" ]

4278986

2 2139493

[ "4278986 2 2139493", "2139493 2139493 1" ]

3992574

2 3 665429

[ "3992574 2 1996287", "1996287 3 665429", "665429 665429 1" ]

4199317

23 182579

[ "4199317 23 182579", "182579 182579 1" ]

3263351

7 7 13 47 109

[ "3263351 7 466193", "466193 7 66599", "66599 13 5123", "5123 47 109", "109 109 1" ]

2248248

2 2 2 3 113 829

[ "2248248 2 1124124", "1124124 2 562062", "562062 2 281031", "281031 3 93677", "93677 113 829", "829 829 1" ]

2734242

2 3 7 65101

[ "2734242 2 1367121", "1367121 3 455707", "455707 7 65101", "65101 65101 1" ]

240243

3 73 1097

[ "240243 3 80081", "80081 73 1097", "1097 1097 1" ]

2395201

79 30319

[ "2395201 79 30319", "30319 30319 1" ]

131408

2 2 2 2 43 191

[ "131408 2 65704", "65704 2 32852", "32852 2 16426", "16426 2 8213", "8213 43 191", "191 191 1" ]

4590007

[ "4590007 4590007 1" ]

376705

5 7 47 229

[ "376705 5 75341", "75341 7 10763", "10763 47 229", "229 229 1" ]

2987709

3 995903

[ "2987709 3 995903", "995903 995903 1" ]

287592

2 2 2 3 23 521

[ "287592 2 143796", "143796 2 71898", "71898 2 35949", "35949 3 11983", "11983 23 521", "521 521 1" ]

1268494

2 634247

[ "1268494 2 634247", "634247 634247 1" ]

856431

3 3 43 2213

[ "856431 3 285477", "285477 3 95159", "95159 43 2213", "2213 2213 1" ]

3662014

2 23 79609

[ "3662014 2 1831007", "1831007 23 79609", "79609 79609 1" ]

4011675

3 5 5 89 601

[ "4011675 3 1337225", "1337225 5 267445", "267445 5 53489", "53489 89 601", "601 601 1" ]

4424396

2 2 1106099

[ "4424396 2 2212198", "2212198 2 1106099", "1106099 1106099 1" ]

2964263

23 359 359

[ "2964263 23 128881", "128881 359 359", "359 359 1" ]

2980751

317 9403

[ "2980751 317 9403", "9403 9403 1" ]

1125160

2 2 2 5 23 1223

[ "1125160 2 562580", "562580 2 281290", "281290 2 140645", "140645 5 28129", "28129 23 1223", "1223 1223 1" ]

1934776

2 2 2 241847

[ "1934776 2 967388", "967388 2 483694", "483694 2 241847", "241847 241847 1" ]

3250927

17 191231

[ "3250927 17 191231", "191231 191231 1" ]

3957523

83 47681

[ "3957523 83 47681", "47681 47681 1" ]

2805889

131 21419

[ "2805889 131 21419", "21419 21419 1" ]

3994184

2 2 2 17 43 683

[ "3994184 2 1997092", "1997092 2 998546", "998546 2 499273", "499273 17 29369", "29369 43 683", "683 683 1" ]