yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
3517652	2 2 879413	[ "3517652 2 1758826", "1758826 2 879413", "879413 879413 1" ]
3496536	2 2 2 3 3 48563	[ "3496536 2 1748268", "1748268 2 874134", "874134 2 437067", "437067 3 145689", "145689 3 48563", "48563 48563 1" ]
1379465	5 17 16229	[ "1379465 5 275893", "275893 17 16229", "16229 16229 1" ]
1023893	13 17 41 113	[ "1023893 13 78761", "78761 17 4633", "4633 41 113", "113 113 1" ]
3613911	3 7 17 53 191	[ "3613911 3 1204637", "1204637 7 172091", "172091 17 10123", "10123 53 191", "191 191 1" ]
3477938	2 1738969	[ "3477938 2 1738969", "1738969 1738969 1" ]
4293278	2 11 19 10271	[ "4293278 2 2146639", "2146639 11 195149", "195149 19 10271", "10271 10271 1" ]
3113117	7 7 63533	[ "3113117 7 444731", "444731 7 63533", "63533 63533 1" ]
1771160	2 2 2 5 44279	[ "1771160 2 885580", "885580 2 442790", "442790 2 221395", "221395 5 44279", "44279 44279 1" ]
725618	2 41 8849	[ "725618 2 362809", "362809 41 8849", "8849 8849 1" ]
4033818	2 3 3 224101	[ "4033818 2 2016909", "2016909 3 672303", "672303 3 224101", "224101 224101 1" ]
3010290	2 3 5 100343	[ "3010290 2 1505145", "1505145 3 501715", "501715 5 100343", "100343 100343 1" ]
2051038	2 11 93229	[ "2051038 2 1025519", "1025519 11 93229", "93229 93229 1" ]
1558739	7 7 13 2447	[ "1558739 7 222677", "222677 7 31811", "31811 13 2447", "2447 2447 1" ]
4325508	2 2 3 3 3 11 11 331	[ "4325508 2 2162754", "2162754 2 1081377", "1081377 3 360459", "360459 3 120153", "120153 3 40051", "40051 11 3641", "3641 11 331", "331 331 1" ]
13098	2 3 37 59	[ "13098 2 6549", "6549 3 2183", "2183 37 59", "59 59 1" ]
3546067	7 587 863	[ "3546067 7 506581", "506581 587 863", "863 863 1" ]
2647633	431 6143	[ "2647633 431 6143", "6143 6143 1" ]
4500618	2 3 373 2011	[ "4500618 2 2250309", "2250309 3 750103", "750103 373 2011", "2011 2011 1" ]
1913396	2 2 233 2053	[ "1913396 2 956698", "956698 2 478349", "478349 233 2053", "2053 2053 1" ]
1756847	941 1867	[ "1756847 941 1867", "1867 1867 1" ]
1068196	2 2 267049	[ "1068196 2 534098", "534098 2 267049", "267049 267049 1" ]
4936977	3 3 3 182851	[ "4936977 3 1645659", "1645659 3 548553", "548553 3 182851", "182851 182851 1" ]
1371766	2 11 23 2711	[ "1371766 2 685883", "685883 11 62353", "62353 23 2711", "2711 2711 1" ]
1198341	3 3 3 44383	[ "1198341 3 399447", "399447 3 133149", "133149 3 44383", "44383 44383 1" ]
2315630	2 5 231563	[ "2315630 2 1157815", "1157815 5 231563", "231563 231563 1" ]
4581660	2 2 3 5 19 4019	[ "4581660 2 2290830", "2290830 2 1145415", "1145415 3 381805", "381805 5 76361", "76361 19 4019", "4019 4019 1" ]
361673	13 43 647	[ "361673 13 27821", "27821 43 647", "647 647 1" ]
4906941	3 13 47 2677	[ "4906941 3 1635647", "1635647 13 125819", "125819 47 2677", "2677 2677 1" ]
4322006	2 13 13 19 673	[ "4322006 2 2161003", "2161003 13 166231", "166231 13 12787", "12787 19 673", "673 673 1" ]
2803402	2 7 17 11779	[ "2803402 2 1401701", "1401701 7 200243", "200243 17 11779", "11779 11779 1" ]
3263197	7 466171	[ "3263197 7 466171", "466171 466171 1" ]
2058745	5 13 19 1667	[ "2058745 5 411749", "411749 13 31673", "31673 19 1667", "1667 1667 1" ]
3579055	5 715811	[ "3579055 5 715811", "715811 715811 1" ]
1061535	3 5 70769	[ "1061535 3 353845", "353845 5 70769", "70769 70769 1" ]
2708308	2 2 677077	[ "2708308 2 1354154", "1354154 2 677077", "677077 677077 1" ]
1523420	2 2 5 19 19 211	[ "1523420 2 761710", "761710 2 380855", "380855 5 76171", "76171 19 4009", "4009 19 211", "211 211 1" ]
3219125	5 5 5 7 13 283	[ "3219125 5 643825", "643825 5 128765", "128765 5 25753", "25753 7 3679", "3679 13 283", "283 283 1" ]
3529491	3 7 168071	[ "3529491 3 1176497", "1176497 7 168071", "168071 168071 1" ]
847286	2 11 19 2027	[ "847286 2 423643", "423643 11 38513", "38513 19 2027", "2027 2027 1" ]
3291153	3 1097051	[ "3291153 3 1097051", "1097051 1097051 1" ]
2472913	397 6229	[ "2472913 397 6229", "6229 6229 1" ]
2809327	2809327	[ "2809327 2809327 1" ]
4487349	3 1495783	[ "4487349 3 1495783", "1495783 1495783 1" ]
2045389	17 79 1523	[ "2045389 17 120317", "120317 79 1523", "1523 1523 1" ]
2309799	3 37 20809	[ "2309799 3 769933", "769933 37 20809", "20809 20809 1" ]
3229482	2 3 538247	[ "3229482 2 1614741", "1614741 3 538247", "538247 538247 1" ]
1378244	2 2 7 49223	[ "1378244 2 689122", "689122 2 344561", "344561 7 49223", "49223 49223 1" ]
1322478	2 3 3 73471	[ "1322478 2 661239", "661239 3 220413", "220413 3 73471", "73471 73471 1" ]
4160591	4160591	[ "4160591 4160591 1" ]
4772886	2 3 17 73 641	[ "4772886 2 2386443", "2386443 3 795481", "795481 17 46793", "46793 73 641", "641 641 1" ]
307420	2 2 5 19 809	[ "307420 2 153710", "153710 2 76855", "76855 5 15371", "15371 19 809", "809 809 1" ]
2957865	3 5 31 6361	[ "2957865 3 985955", "985955 5 197191", "197191 31 6361", "6361 6361 1" ]
871144	2 2 2 108893	[ "871144 2 435572", "435572 2 217786", "217786 2 108893", "108893 108893 1" ]
946891	11 59 1459	[ "946891 11 86081", "86081 59 1459", "1459 1459 1" ]
4641825	3 5 5 59 1049	[ "4641825 3 1547275", "1547275 5 309455", "309455 5 61891", "61891 59 1049", "1049 1049 1" ]
3652115	5 29 89 283	[ "3652115 5 730423", "730423 29 25187", "25187 89 283", "283 283 1" ]
3935729	7 7 31 2591	[ "3935729 7 562247", "562247 7 80321", "80321 31 2591", "2591 2591 1" ]
4716623	2141 2203	[ "4716623 2141 2203", "2203 2203 1" ]
2437378	2 83 14683	[ "2437378 2 1218689", "1218689 83 14683", "14683 14683 1" ]
195476	2 2 48869	[ "195476 2 97738", "97738 2 48869", "48869 48869 1" ]
3374768	2 2 2 2 210923	[ "3374768 2 1687384", "1687384 2 843692", "843692 2 421846", "421846 2 210923", "210923 210923 1" ]
2101040	2 2 2 2 5 26263	[ "2101040 2 1050520", "1050520 2 525260", "525260 2 262630", "262630 2 131315", "131315 5 26263", "26263 26263 1" ]
4725882	2 3 3 7 37507	[ "4725882 2 2362941", "2362941 3 787647", "787647 3 262549", "262549 7 37507", "37507 37507 1" ]
1444407	3 481469	[ "1444407 3 481469", "481469 481469 1" ]
4116200	2 2 2 5 5 11 1871	[ "4116200 2 2058100", "2058100 2 1029050", "1029050 2 514525", "514525 5 102905", "102905 5 20581", "20581 11 1871", "1871 1871 1" ]
4942183	4942183	[ "4942183 4942183 1" ]
3587667	3 1039 1151	[ "3587667 3 1195889", "1195889 1039 1151", "1151 1151 1" ]
3293951	1453 2267	[ "3293951 1453 2267", "2267 2267 1" ]
3499124	2 2 89 9829	[ "3499124 2 1749562", "1749562 2 874781", "874781 89 9829", "9829 9829 1" ]
1754235	3 3 5 7 5569	[ "1754235 3 584745", "584745 3 194915", "194915 5 38983", "38983 7 5569", "5569 5569 1" ]
1904844	2 2 3 181 877	[ "1904844 2 952422", "952422 2 476211", "476211 3 158737", "158737 181 877", "877 877 1" ]
496067	11 13 3469	[ "496067 11 45097", "45097 13 3469", "3469 3469 1" ]
4723881	3 1574627	[ "4723881 3 1574627", "1574627 1574627 1" ]
2880235	5 397 1451	[ "2880235 5 576047", "576047 397 1451", "1451 1451 1" ]
3235773	3 89 12119	[ "3235773 3 1078591", "1078591 89 12119", "12119 12119 1" ]
1845062	2 922531	[ "1845062 2 922531", "922531 922531 1" ]
1791897	3 457 1307	[ "1791897 3 597299", "597299 457 1307", "1307 1307 1" ]
431951	13 149 223	[ "431951 13 33227", "33227 149 223", "223 223 1" ]
1498729	1498729	[ "1498729 1498729 1" ]
3302351	13 254027	[ "3302351 13 254027", "254027 254027 1" ]
1733672	2 2 2 37 5857	[ "1733672 2 866836", "866836 2 433418", "433418 2 216709", "216709 37 5857", "5857 5857 1" ]
3140017	1321 2377	[ "3140017 1321 2377", "2377 2377 1" ]
2794926	2 3 465821	[ "2794926 2 1397463", "1397463 3 465821", "465821 465821 1" ]
887577	3 191 1549	[ "887577 3 295859", "295859 191 1549", "1549 1549 1" ]
3126348	2 2 3 3 86843	[ "3126348 2 1563174", "1563174 2 781587", "781587 3 260529", "260529 3 86843", "86843 86843 1" ]
2700485	5 71 7607	[ "2700485 5 540097", "540097 71 7607", "7607 7607 1" ]
1172582	2 586291	[ "1172582 2 586291", "586291 586291 1" ]
3115021	7 13 34231	[ "3115021 7 445003", "445003 13 34231", "34231 34231 1" ]
987441	3 7 13 3617	[ "987441 3 329147", "329147 7 47021", "47021 13 3617", "3617 3617 1" ]
3703386	2 3 617231	[ "3703386 2 1851693", "1851693 3 617231", "617231 617231 1" ]
2473317	3 3 7 11 43 83	[ "2473317 3 824439", "824439 3 274813", "274813 7 39259", "39259 11 3569", "3569 43 83", "83 83 1" ]
1875376	2 2 2 2 19 31 199	[ "1875376 2 937688", "937688 2 468844", "468844 2 234422", "234422 2 117211", "117211 19 6169", "6169 31 199", "199 199 1" ]
3911819	17 230107	[ "3911819 17 230107", "230107 230107 1" ]
2031796	2 2 13 41 953	[ "2031796 2 1015898", "1015898 2 507949", "507949 13 39073", "39073 41 953", "953 953 1" ]
2663652	2 2 3 67 3313	[ "2663652 2 1331826", "1331826 2 665913", "665913 3 221971", "221971 67 3313", "3313 3313 1" ]
1889770	2 5 59 3203	[ "1889770 2 944885", "944885 5 188977", "188977 59 3203", "3203 3203 1" ]
404007	3 134669	[ "404007 3 134669", "134669 134669 1" ]
2757509	83 33223	[ "2757509 83 33223", "33223 33223 1" ]
4766579	17 257 1091	[ "4766579 17 280387", "280387 257 1091", "1091 1091 1" ]

3517652

2 2 879413

[ "3517652 2 1758826", "1758826 2 879413", "879413 879413 1" ]

3496536

2 2 2 3 3 48563

[ "3496536 2 1748268", "1748268 2 874134", "874134 2 437067", "437067 3 145689", "145689 3 48563", "48563 48563 1" ]

1379465

5 17 16229

[ "1379465 5 275893", "275893 17 16229", "16229 16229 1" ]

1023893

13 17 41 113

[ "1023893 13 78761", "78761 17 4633", "4633 41 113", "113 113 1" ]

3613911

3 7 17 53 191

[ "3613911 3 1204637", "1204637 7 172091", "172091 17 10123", "10123 53 191", "191 191 1" ]

3477938

2 1738969

[ "3477938 2 1738969", "1738969 1738969 1" ]

4293278

2 11 19 10271

[ "4293278 2 2146639", "2146639 11 195149", "195149 19 10271", "10271 10271 1" ]

3113117

7 7 63533

[ "3113117 7 444731", "444731 7 63533", "63533 63533 1" ]

1771160

2 2 2 5 44279

[ "1771160 2 885580", "885580 2 442790", "442790 2 221395", "221395 5 44279", "44279 44279 1" ]

725618

2 41 8849

[ "725618 2 362809", "362809 41 8849", "8849 8849 1" ]

4033818

2 3 3 224101

[ "4033818 2 2016909", "2016909 3 672303", "672303 3 224101", "224101 224101 1" ]

3010290

2 3 5 100343

[ "3010290 2 1505145", "1505145 3 501715", "501715 5 100343", "100343 100343 1" ]

2051038

2 11 93229

[ "2051038 2 1025519", "1025519 11 93229", "93229 93229 1" ]

1558739

7 7 13 2447

[ "1558739 7 222677", "222677 7 31811", "31811 13 2447", "2447 2447 1" ]

4325508

2 2 3 3 3 11 11 331

[ "4325508 2 2162754", "2162754 2 1081377", "1081377 3 360459", "360459 3 120153", "120153 3 40051", "40051 11 3641", "3641 11 331", "331 331 1" ]

13098

2 3 37 59

[ "13098 2 6549", "6549 3 2183", "2183 37 59", "59 59 1" ]

3546067

7 587 863

[ "3546067 7 506581", "506581 587 863", "863 863 1" ]

2647633

431 6143

[ "2647633 431 6143", "6143 6143 1" ]

4500618

2 3 373 2011

[ "4500618 2 2250309", "2250309 3 750103", "750103 373 2011", "2011 2011 1" ]

1913396

2 2 233 2053

[ "1913396 2 956698", "956698 2 478349", "478349 233 2053", "2053 2053 1" ]

1756847

941 1867

[ "1756847 941 1867", "1867 1867 1" ]

1068196

2 2 267049

[ "1068196 2 534098", "534098 2 267049", "267049 267049 1" ]

4936977

3 3 3 182851

[ "4936977 3 1645659", "1645659 3 548553", "548553 3 182851", "182851 182851 1" ]

1371766

2 11 23 2711

[ "1371766 2 685883", "685883 11 62353", "62353 23 2711", "2711 2711 1" ]

1198341

3 3 3 44383

[ "1198341 3 399447", "399447 3 133149", "133149 3 44383", "44383 44383 1" ]

2315630

2 5 231563

[ "2315630 2 1157815", "1157815 5 231563", "231563 231563 1" ]

4581660

2 2 3 5 19 4019

[ "4581660 2 2290830", "2290830 2 1145415", "1145415 3 381805", "381805 5 76361", "76361 19 4019", "4019 4019 1" ]

361673

13 43 647

[ "361673 13 27821", "27821 43 647", "647 647 1" ]

4906941

3 13 47 2677

[ "4906941 3 1635647", "1635647 13 125819", "125819 47 2677", "2677 2677 1" ]

4322006

2 13 13 19 673

[ "4322006 2 2161003", "2161003 13 166231", "166231 13 12787", "12787 19 673", "673 673 1" ]

2803402

2 7 17 11779

[ "2803402 2 1401701", "1401701 7 200243", "200243 17 11779", "11779 11779 1" ]

3263197

7 466171

[ "3263197 7 466171", "466171 466171 1" ]

2058745

5 13 19 1667

[ "2058745 5 411749", "411749 13 31673", "31673 19 1667", "1667 1667 1" ]

3579055

5 715811

[ "3579055 5 715811", "715811 715811 1" ]

1061535

3 5 70769

[ "1061535 3 353845", "353845 5 70769", "70769 70769 1" ]

2708308

2 2 677077

[ "2708308 2 1354154", "1354154 2 677077", "677077 677077 1" ]

1523420

2 2 5 19 19 211

[ "1523420 2 761710", "761710 2 380855", "380855 5 76171", "76171 19 4009", "4009 19 211", "211 211 1" ]

3219125

5 5 5 7 13 283

[ "3219125 5 643825", "643825 5 128765", "128765 5 25753", "25753 7 3679", "3679 13 283", "283 283 1" ]

3529491

3 7 168071

[ "3529491 3 1176497", "1176497 7 168071", "168071 168071 1" ]

847286

2 11 19 2027

[ "847286 2 423643", "423643 11 38513", "38513 19 2027", "2027 2027 1" ]

3291153

3 1097051

[ "3291153 3 1097051", "1097051 1097051 1" ]

2472913

397 6229

[ "2472913 397 6229", "6229 6229 1" ]

2809327

[ "2809327 2809327 1" ]

4487349

3 1495783

[ "4487349 3 1495783", "1495783 1495783 1" ]

2045389

17 79 1523

[ "2045389 17 120317", "120317 79 1523", "1523 1523 1" ]

2309799

3 37 20809

[ "2309799 3 769933", "769933 37 20809", "20809 20809 1" ]

3229482

2 3 538247

[ "3229482 2 1614741", "1614741 3 538247", "538247 538247 1" ]

1378244

2 2 7 49223

[ "1378244 2 689122", "689122 2 344561", "344561 7 49223", "49223 49223 1" ]

1322478

2 3 3 73471

[ "1322478 2 661239", "661239 3 220413", "220413 3 73471", "73471 73471 1" ]

4160591

[ "4160591 4160591 1" ]

4772886

2 3 17 73 641

[ "4772886 2 2386443", "2386443 3 795481", "795481 17 46793", "46793 73 641", "641 641 1" ]

307420

2 2 5 19 809

[ "307420 2 153710", "153710 2 76855", "76855 5 15371", "15371 19 809", "809 809 1" ]

2957865

3 5 31 6361

[ "2957865 3 985955", "985955 5 197191", "197191 31 6361", "6361 6361 1" ]

871144

2 2 2 108893

[ "871144 2 435572", "435572 2 217786", "217786 2 108893", "108893 108893 1" ]

946891

11 59 1459

[ "946891 11 86081", "86081 59 1459", "1459 1459 1" ]

4641825

3 5 5 59 1049

[ "4641825 3 1547275", "1547275 5 309455", "309455 5 61891", "61891 59 1049", "1049 1049 1" ]

3652115

5 29 89 283

[ "3652115 5 730423", "730423 29 25187", "25187 89 283", "283 283 1" ]

3935729

7 7 31 2591

[ "3935729 7 562247", "562247 7 80321", "80321 31 2591", "2591 2591 1" ]

4716623

2141 2203

[ "4716623 2141 2203", "2203 2203 1" ]

2437378

2 83 14683

[ "2437378 2 1218689", "1218689 83 14683", "14683 14683 1" ]

195476

2 2 48869

[ "195476 2 97738", "97738 2 48869", "48869 48869 1" ]

3374768

2 2 2 2 210923

[ "3374768 2 1687384", "1687384 2 843692", "843692 2 421846", "421846 2 210923", "210923 210923 1" ]

2101040

2 2 2 2 5 26263

[ "2101040 2 1050520", "1050520 2 525260", "525260 2 262630", "262630 2 131315", "131315 5 26263", "26263 26263 1" ]

4725882

2 3 3 7 37507

[ "4725882 2 2362941", "2362941 3 787647", "787647 3 262549", "262549 7 37507", "37507 37507 1" ]

1444407

3 481469

[ "1444407 3 481469", "481469 481469 1" ]

4116200

2 2 2 5 5 11 1871

[ "4116200 2 2058100", "2058100 2 1029050", "1029050 2 514525", "514525 5 102905", "102905 5 20581", "20581 11 1871", "1871 1871 1" ]

4942183

[ "4942183 4942183 1" ]

3587667

3 1039 1151

[ "3587667 3 1195889", "1195889 1039 1151", "1151 1151 1" ]

3293951

1453 2267

[ "3293951 1453 2267", "2267 2267 1" ]

3499124

2 2 89 9829

[ "3499124 2 1749562", "1749562 2 874781", "874781 89 9829", "9829 9829 1" ]

1754235

3 3 5 7 5569

[ "1754235 3 584745", "584745 3 194915", "194915 5 38983", "38983 7 5569", "5569 5569 1" ]

1904844

2 2 3 181 877

[ "1904844 2 952422", "952422 2 476211", "476211 3 158737", "158737 181 877", "877 877 1" ]

496067

11 13 3469

[ "496067 11 45097", "45097 13 3469", "3469 3469 1" ]

4723881

3 1574627

[ "4723881 3 1574627", "1574627 1574627 1" ]

2880235

5 397 1451

[ "2880235 5 576047", "576047 397 1451", "1451 1451 1" ]

3235773

3 89 12119

[ "3235773 3 1078591", "1078591 89 12119", "12119 12119 1" ]

1845062

2 922531

[ "1845062 2 922531", "922531 922531 1" ]

1791897

3 457 1307

[ "1791897 3 597299", "597299 457 1307", "1307 1307 1" ]

431951

13 149 223

[ "431951 13 33227", "33227 149 223", "223 223 1" ]

1498729

[ "1498729 1498729 1" ]

3302351

13 254027

[ "3302351 13 254027", "254027 254027 1" ]

1733672

2 2 2 37 5857

[ "1733672 2 866836", "866836 2 433418", "433418 2 216709", "216709 37 5857", "5857 5857 1" ]

3140017

1321 2377

[ "3140017 1321 2377", "2377 2377 1" ]

2794926

2 3 465821

[ "2794926 2 1397463", "1397463 3 465821", "465821 465821 1" ]

887577

3 191 1549

[ "887577 3 295859", "295859 191 1549", "1549 1549 1" ]

3126348

2 2 3 3 86843

[ "3126348 2 1563174", "1563174 2 781587", "781587 3 260529", "260529 3 86843", "86843 86843 1" ]

2700485

5 71 7607

[ "2700485 5 540097", "540097 71 7607", "7607 7607 1" ]

1172582

2 586291

[ "1172582 2 586291", "586291 586291 1" ]

3115021

7 13 34231

[ "3115021 7 445003", "445003 13 34231", "34231 34231 1" ]

987441

3 7 13 3617

[ "987441 3 329147", "329147 7 47021", "47021 13 3617", "3617 3617 1" ]

3703386

2 3 617231

[ "3703386 2 1851693", "1851693 3 617231", "617231 617231 1" ]

2473317

3 3 7 11 43 83

[ "2473317 3 824439", "824439 3 274813", "274813 7 39259", "39259 11 3569", "3569 43 83", "83 83 1" ]

1875376

2 2 2 2 19 31 199

[ "1875376 2 937688", "937688 2 468844", "468844 2 234422", "234422 2 117211", "117211 19 6169", "6169 31 199", "199 199 1" ]

3911819

17 230107

[ "3911819 17 230107", "230107 230107 1" ]

2031796

2 2 13 41 953

[ "2031796 2 1015898", "1015898 2 507949", "507949 13 39073", "39073 41 953", "953 953 1" ]

2663652

2 2 3 67 3313

[ "2663652 2 1331826", "1331826 2 665913", "665913 3 221971", "221971 67 3313", "3313 3313 1" ]

1889770

2 5 59 3203

[ "1889770 2 944885", "944885 5 188977", "188977 59 3203", "3203 3203 1" ]

404007

3 134669

[ "404007 3 134669", "134669 134669 1" ]

2757509

83 33223

[ "2757509 83 33223", "33223 33223 1" ]

4766579

17 257 1091

[ "4766579 17 280387", "280387 257 1091", "1091 1091 1" ]