yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
843414	2 3 11 13 983	[ "843414 2 421707", "421707 3 140569", "140569 11 12779", "12779 13 983", "983 983 1" ]
3491699	23 151813	[ "3491699 23 151813", "151813 151813 1" ]
3603139	1009 3571	[ "3603139 1009 3571", "3571 3571 1" ]
1980649	11 11 16369	[ "1980649 11 180059", "180059 11 16369", "16369 16369 1" ]
2185956	2 2 3 3 41 1481	[ "2185956 2 1092978", "1092978 2 546489", "546489 3 182163", "182163 3 60721", "60721 41 1481", "1481 1481 1" ]
2493261	3 3 3 3 30781	[ "2493261 3 831087", "831087 3 277029", "277029 3 92343", "92343 3 30781", "30781 30781 1" ]
745908	2 2 3 61 1019	[ "745908 2 372954", "372954 2 186477", "186477 3 62159", "62159 61 1019", "1019 1019 1" ]
4066076	2 2 7 19 7643	[ "4066076 2 2033038", "2033038 2 1016519", "1016519 7 145217", "145217 19 7643", "7643 7643 1" ]
4812195	3 5 541 593	[ "4812195 3 1604065", "1604065 5 320813", "320813 541 593", "593 593 1" ]
4965653	7 11 64489	[ "4965653 7 709379", "709379 11 64489", "64489 64489 1" ]
3941089	83 103 461	[ "3941089 83 47483", "47483 103 461", "461 461 1" ]
1248728	2 2 2 13 12007	[ "1248728 2 624364", "624364 2 312182", "312182 2 156091", "156091 13 12007", "12007 12007 1" ]
951918	2 3 11 14423	[ "951918 2 475959", "475959 3 158653", "158653 11 14423", "14423 14423 1" ]
4481147	11 407377	[ "4481147 11 407377", "407377 407377 1" ]
3404154	2 3 13 19 2297	[ "3404154 2 1702077", "1702077 3 567359", "567359 13 43643", "43643 19 2297", "2297 2297 1" ]
1288416	2 2 2 2 2 3 13421	[ "1288416 2 644208", "644208 2 322104", "322104 2 161052", "161052 2 80526", "80526 2 40263", "40263 3 13421", "13421 13421 1" ]
2953478	2 11 17 53 149	[ "2953478 2 1476739", "1476739 11 134249", "134249 17 7897", "7897 53 149", "149 149 1" ]
3216571	3216571	[ "3216571 3216571 1" ]
3499780	2 2 5 174989	[ "3499780 2 1749890", "1749890 2 874945", "874945 5 174989", "174989 174989 1" ]
4174895	5 37 22567	[ "4174895 5 834979", "834979 37 22567", "22567 22567 1" ]
4762728	2 2 2 3 3 29 2281	[ "4762728 2 2381364", "2381364 2 1190682", "1190682 2 595341", "595341 3 198447", "198447 3 66149", "66149 29 2281", "2281 2281 1" ]
4314514	2 2157257	[ "4314514 2 2157257", "2157257 2157257 1" ]
3611594	2 7 7 137 269	[ "3611594 2 1805797", "1805797 7 257971", "257971 7 36853", "36853 137 269", "269 269 1" ]
3507352	2 2 2 438419	[ "3507352 2 1753676", "1753676 2 876838", "876838 2 438419", "438419 438419 1" ]
1322058	2 3 19 11597	[ "1322058 2 661029", "661029 3 220343", "220343 19 11597", "11597 11597 1" ]
2276566	2 41 27763	[ "2276566 2 1138283", "1138283 41 27763", "27763 27763 1" ]
990445	5 113 1753	[ "990445 5 198089", "198089 113 1753", "1753 1753 1" ]
1358891	1358891	[ "1358891 1358891 1" ]
2231391	3 23 73 443	[ "2231391 3 743797", "743797 23 32339", "32339 73 443", "443 443 1" ]
1482518	2 151 4909	[ "1482518 2 741259", "741259 151 4909", "4909 4909 1" ]
3971647	139 28573	[ "3971647 139 28573", "28573 28573 1" ]
2409456	2 2 2 2 3 7 71 101	[ "2409456 2 1204728", "1204728 2 602364", "602364 2 301182", "301182 2 150591", "150591 3 50197", "50197 7 7171", "7171 71 101", "101 101 1" ]
4863827	4863827	[ "4863827 4863827 1" ]
62856	2 2 2 3 3 3 3 97	[ "62856 2 31428", "31428 2 15714", "15714 2 7857", "7857 3 2619", "2619 3 873", "873 3 291", "291 3 97", "97 97 1" ]
467516	2 2 7 59 283	[ "467516 2 233758", "233758 2 116879", "116879 7 16697", "16697 59 283", "283 283 1" ]
4907930	2 5 163 3011	[ "4907930 2 2453965", "2453965 5 490793", "490793 163 3011", "3011 3011 1" ]
2168776	2 2 2 271097	[ "2168776 2 1084388", "1084388 2 542194", "542194 2 271097", "271097 271097 1" ]
520077	3 173359	[ "520077 3 173359", "173359 173359 1" ]
721297	19 37963	[ "721297 19 37963", "37963 37963 1" ]
780770	2 5 163 479	[ "780770 2 390385", "390385 5 78077", "78077 163 479", "479 479 1" ]
633162	2 3 105527	[ "633162 2 316581", "316581 3 105527", "105527 105527 1" ]
1310984	2 2 2 37 43 103	[ "1310984 2 655492", "655492 2 327746", "327746 2 163873", "163873 37 4429", "4429 43 103", "103 103 1" ]
847398	2 3 141233	[ "847398 2 423699", "423699 3 141233", "141233 141233 1" ]
4085295	3 5 272353	[ "4085295 3 1361765", "1361765 5 272353", "272353 272353 1" ]
2705801	7 386543	[ "2705801 7 386543", "386543 386543 1" ]
4329762	2 3 193 3739	[ "4329762 2 2164881", "2164881 3 721627", "721627 193 3739", "3739 3739 1" ]
1605111	3 535037	[ "1605111 3 535037", "535037 535037 1" ]
1283033	409 3137	[ "1283033 409 3137", "3137 3137 1" ]
1581148	2 2 395287	[ "1581148 2 790574", "790574 2 395287", "395287 395287 1" ]
831727	13 137 467	[ "831727 13 63979", "63979 137 467", "467 467 1" ]
3569424	2 2 2 2 3 74363	[ "3569424 2 1784712", "1784712 2 892356", "892356 2 446178", "446178 2 223089", "223089 3 74363", "74363 74363 1" ]
708489	3 3 78721	[ "708489 3 236163", "236163 3 78721", "78721 78721 1" ]
2370524	2 2 13 45587	[ "2370524 2 1185262", "1185262 2 592631", "592631 13 45587", "45587 45587 1" ]
2901058	2 251 5779	[ "2901058 2 1450529", "1450529 251 5779", "5779 5779 1" ]
778133	337 2309	[ "778133 337 2309", "2309 2309 1" ]
4696786	2 389 6037	[ "4696786 2 2348393", "2348393 389 6037", "6037 6037 1" ]
417945	3 5 11 17 149	[ "417945 3 139315", "139315 5 27863", "27863 11 2533", "2533 17 149", "149 149 1" ]
3600216	2 2 2 3 3 31 1613	[ "3600216 2 1800108", "1800108 2 900054", "900054 2 450027", "450027 3 150009", "150009 3 50003", "50003 31 1613", "1613 1613 1" ]
2910734	2 1455367	[ "2910734 2 1455367", "1455367 1455367 1" ]
597304	2 2 2 197 379	[ "597304 2 298652", "298652 2 149326", "149326 2 74663", "74663 197 379", "379 379 1" ]
442135	5 88427	[ "442135 5 88427", "88427 88427 1" ]
3654939	3 1218313	[ "3654939 3 1218313", "1218313 1218313 1" ]
1364345	5 353 773	[ "1364345 5 272869", "272869 353 773", "773 773 1" ]
1848898	2 571 1619	[ "1848898 2 924449", "924449 571 1619", "1619 1619 1" ]
2340760	2 2 2 5 139 421	[ "2340760 2 1170380", "1170380 2 585190", "585190 2 292595", "292595 5 58519", "58519 139 421", "421 421 1" ]
4622120	2 2 2 5 115553	[ "4622120 2 2311060", "2311060 2 1155530", "1155530 2 577765", "577765 5 115553", "115553 115553 1" ]
4078433	607 6719	[ "4078433 607 6719", "6719 6719 1" ]
1597384	2 2 2 199673	[ "1597384 2 798692", "798692 2 399346", "399346 2 199673", "199673 199673 1" ]
3970913	89 44617	[ "3970913 89 44617", "44617 44617 1" ]
2651038	2 13 101963	[ "2651038 2 1325519", "1325519 13 101963", "101963 101963 1" ]
3506296	2 2 2 438287	[ "3506296 2 1753148", "1753148 2 876574", "876574 2 438287", "438287 438287 1" ]
4666408	2 2 2 583301	[ "4666408 2 2333204", "2333204 2 1166602", "1166602 2 583301", "583301 583301 1" ]
4654049	4654049	[ "4654049 4654049 1" ]
4337472	2 2 2 2 2 2 3 19 29 41	[ "4337472 2 2168736", "2168736 2 1084368", "1084368 2 542184", "542184 2 271092", "271092 2 135546", "135546 2 67773", "67773 3 22591", "22591 19 1189", "1189 29 41", "41 41 1" ]
1029852	2 2 3 3 28607	[ "1029852 2 514926", "514926 2 257463", "257463 3 85821", "85821 3 28607", "28607 28607 1" ]
2823281	1171 2411	[ "2823281 1171 2411", "2411 2411 1" ]
3694960	2 2 2 2 5 46187	[ "3694960 2 1847480", "1847480 2 923740", "923740 2 461870", "461870 2 230935", "230935 5 46187", "46187 46187 1" ]
1680932	2 2 11 11 23 151	[ "1680932 2 840466", "840466 2 420233", "420233 11 38203", "38203 11 3473", "3473 23 151", "151 151 1" ]
4419581	4419581	[ "4419581 4419581 1" ]
2626174	2 1313087	[ "2626174 2 1313087", "1313087 1313087 1" ]
3464274	2 3 11 52489	[ "3464274 2 1732137", "1732137 3 577379", "577379 11 52489", "52489 52489 1" ]
1123659	3 3 3 41617	[ "1123659 3 374553", "374553 3 124851", "124851 3 41617", "41617 41617 1" ]
3947038	2 1973519	[ "3947038 2 1973519", "1973519 1973519 1" ]
1538522	2 769261	[ "1538522 2 769261", "769261 769261 1" ]
3135149	1559 2011	[ "3135149 1559 2011", "2011 2011 1" ]
215098	2 13 8273	[ "215098 2 107549", "107549 13 8273", "8273 8273 1" ]
599892	2 2 3 49991	[ "599892 2 299946", "299946 2 149973", "149973 3 49991", "49991 49991 1" ]
246314	2 107 1151	[ "246314 2 123157", "123157 107 1151", "1151 1151 1" ]
289527	3 7 17 811	[ "289527 3 96509", "96509 7 13787", "13787 17 811", "811 811 1" ]
4183603	79 52957	[ "4183603 79 52957", "52957 52957 1" ]
3696163	3696163	[ "3696163 3696163 1" ]
4352159	7 19 43 761	[ "4352159 7 621737", "621737 19 32723", "32723 43 761", "761 761 1" ]
1043700	2 2 3 5 5 7 7 71	[ "1043700 2 521850", "521850 2 260925", "260925 3 86975", "86975 5 17395", "17395 5 3479", "3479 7 497", "497 7 71", "71 71 1" ]
1260092	2 2 211 1493	[ "1260092 2 630046", "630046 2 315023", "315023 211 1493", "1493 1493 1" ]
2695501	151 17851	[ "2695501 151 17851", "17851 17851 1" ]
310989	3 7 59 251	[ "310989 3 103663", "103663 7 14809", "14809 59 251", "251 251 1" ]
2055352	2 2 2 13 19763	[ "2055352 2 1027676", "1027676 2 513838", "513838 2 256919", "256919 13 19763", "19763 19763 1" ]
3593787	3 1197929	[ "3593787 3 1197929", "1197929 1197929 1" ]
4946803	4946803	[ "4946803 4946803 1" ]
2364787	61 38767	[ "2364787 61 38767", "38767 38767 1" ]

843414

2 3 11 13 983

[ "843414 2 421707", "421707 3 140569", "140569 11 12779", "12779 13 983", "983 983 1" ]

3491699

23 151813

[ "3491699 23 151813", "151813 151813 1" ]

3603139

1009 3571

[ "3603139 1009 3571", "3571 3571 1" ]

1980649

11 11 16369

[ "1980649 11 180059", "180059 11 16369", "16369 16369 1" ]

2185956

2 2 3 3 41 1481

[ "2185956 2 1092978", "1092978 2 546489", "546489 3 182163", "182163 3 60721", "60721 41 1481", "1481 1481 1" ]

2493261

3 3 3 3 30781

[ "2493261 3 831087", "831087 3 277029", "277029 3 92343", "92343 3 30781", "30781 30781 1" ]

745908

2 2 3 61 1019

[ "745908 2 372954", "372954 2 186477", "186477 3 62159", "62159 61 1019", "1019 1019 1" ]

4066076

2 2 7 19 7643

[ "4066076 2 2033038", "2033038 2 1016519", "1016519 7 145217", "145217 19 7643", "7643 7643 1" ]

4812195

3 5 541 593

[ "4812195 3 1604065", "1604065 5 320813", "320813 541 593", "593 593 1" ]

4965653

7 11 64489

[ "4965653 7 709379", "709379 11 64489", "64489 64489 1" ]

3941089

83 103 461

[ "3941089 83 47483", "47483 103 461", "461 461 1" ]

1248728

2 2 2 13 12007

[ "1248728 2 624364", "624364 2 312182", "312182 2 156091", "156091 13 12007", "12007 12007 1" ]

951918

2 3 11 14423

[ "951918 2 475959", "475959 3 158653", "158653 11 14423", "14423 14423 1" ]

4481147

11 407377

[ "4481147 11 407377", "407377 407377 1" ]

3404154

2 3 13 19 2297

[ "3404154 2 1702077", "1702077 3 567359", "567359 13 43643", "43643 19 2297", "2297 2297 1" ]

1288416

2 2 2 2 2 3 13421

[ "1288416 2 644208", "644208 2 322104", "322104 2 161052", "161052 2 80526", "80526 2 40263", "40263 3 13421", "13421 13421 1" ]

2953478

2 11 17 53 149

[ "2953478 2 1476739", "1476739 11 134249", "134249 17 7897", "7897 53 149", "149 149 1" ]

3216571

[ "3216571 3216571 1" ]

3499780

2 2 5 174989

[ "3499780 2 1749890", "1749890 2 874945", "874945 5 174989", "174989 174989 1" ]

4174895

5 37 22567

[ "4174895 5 834979", "834979 37 22567", "22567 22567 1" ]

4762728

2 2 2 3 3 29 2281

[ "4762728 2 2381364", "2381364 2 1190682", "1190682 2 595341", "595341 3 198447", "198447 3 66149", "66149 29 2281", "2281 2281 1" ]

4314514

2 2157257

[ "4314514 2 2157257", "2157257 2157257 1" ]

3611594

2 7 7 137 269

[ "3611594 2 1805797", "1805797 7 257971", "257971 7 36853", "36853 137 269", "269 269 1" ]

3507352

2 2 2 438419

[ "3507352 2 1753676", "1753676 2 876838", "876838 2 438419", "438419 438419 1" ]

1322058

2 3 19 11597

[ "1322058 2 661029", "661029 3 220343", "220343 19 11597", "11597 11597 1" ]

2276566

2 41 27763

[ "2276566 2 1138283", "1138283 41 27763", "27763 27763 1" ]

990445

5 113 1753

[ "990445 5 198089", "198089 113 1753", "1753 1753 1" ]

1358891

[ "1358891 1358891 1" ]

2231391

3 23 73 443

[ "2231391 3 743797", "743797 23 32339", "32339 73 443", "443 443 1" ]

1482518

2 151 4909

[ "1482518 2 741259", "741259 151 4909", "4909 4909 1" ]

3971647

139 28573

[ "3971647 139 28573", "28573 28573 1" ]

2409456

2 2 2 2 3 7 71 101

[ "2409456 2 1204728", "1204728 2 602364", "602364 2 301182", "301182 2 150591", "150591 3 50197", "50197 7 7171", "7171 71 101", "101 101 1" ]

4863827

[ "4863827 4863827 1" ]

62856

2 2 2 3 3 3 3 97

[ "62856 2 31428", "31428 2 15714", "15714 2 7857", "7857 3 2619", "2619 3 873", "873 3 291", "291 3 97", "97 97 1" ]

467516

2 2 7 59 283

[ "467516 2 233758", "233758 2 116879", "116879 7 16697", "16697 59 283", "283 283 1" ]

4907930

2 5 163 3011

[ "4907930 2 2453965", "2453965 5 490793", "490793 163 3011", "3011 3011 1" ]

2168776

2 2 2 271097

[ "2168776 2 1084388", "1084388 2 542194", "542194 2 271097", "271097 271097 1" ]

520077

3 173359

[ "520077 3 173359", "173359 173359 1" ]

721297

19 37963

[ "721297 19 37963", "37963 37963 1" ]

780770

2 5 163 479

[ "780770 2 390385", "390385 5 78077", "78077 163 479", "479 479 1" ]

633162

2 3 105527

[ "633162 2 316581", "316581 3 105527", "105527 105527 1" ]

1310984

2 2 2 37 43 103

[ "1310984 2 655492", "655492 2 327746", "327746 2 163873", "163873 37 4429", "4429 43 103", "103 103 1" ]

847398

2 3 141233

[ "847398 2 423699", "423699 3 141233", "141233 141233 1" ]

4085295

3 5 272353

[ "4085295 3 1361765", "1361765 5 272353", "272353 272353 1" ]

2705801

7 386543

[ "2705801 7 386543", "386543 386543 1" ]

4329762

2 3 193 3739

[ "4329762 2 2164881", "2164881 3 721627", "721627 193 3739", "3739 3739 1" ]

1605111

3 535037

[ "1605111 3 535037", "535037 535037 1" ]

1283033

409 3137

[ "1283033 409 3137", "3137 3137 1" ]

1581148

2 2 395287

[ "1581148 2 790574", "790574 2 395287", "395287 395287 1" ]

831727

13 137 467

[ "831727 13 63979", "63979 137 467", "467 467 1" ]

3569424

2 2 2 2 3 74363

[ "3569424 2 1784712", "1784712 2 892356", "892356 2 446178", "446178 2 223089", "223089 3 74363", "74363 74363 1" ]

708489

3 3 78721

[ "708489 3 236163", "236163 3 78721", "78721 78721 1" ]

2370524

2 2 13 45587

[ "2370524 2 1185262", "1185262 2 592631", "592631 13 45587", "45587 45587 1" ]

2901058

2 251 5779

[ "2901058 2 1450529", "1450529 251 5779", "5779 5779 1" ]

778133

337 2309

[ "778133 337 2309", "2309 2309 1" ]

4696786

2 389 6037

[ "4696786 2 2348393", "2348393 389 6037", "6037 6037 1" ]

417945

3 5 11 17 149

[ "417945 3 139315", "139315 5 27863", "27863 11 2533", "2533 17 149", "149 149 1" ]

3600216

2 2 2 3 3 31 1613

[ "3600216 2 1800108", "1800108 2 900054", "900054 2 450027", "450027 3 150009", "150009 3 50003", "50003 31 1613", "1613 1613 1" ]

2910734

2 1455367

[ "2910734 2 1455367", "1455367 1455367 1" ]

597304

2 2 2 197 379

[ "597304 2 298652", "298652 2 149326", "149326 2 74663", "74663 197 379", "379 379 1" ]

442135

5 88427

[ "442135 5 88427", "88427 88427 1" ]

3654939

3 1218313

[ "3654939 3 1218313", "1218313 1218313 1" ]

1364345

5 353 773

[ "1364345 5 272869", "272869 353 773", "773 773 1" ]

1848898

2 571 1619

[ "1848898 2 924449", "924449 571 1619", "1619 1619 1" ]

2340760

2 2 2 5 139 421

[ "2340760 2 1170380", "1170380 2 585190", "585190 2 292595", "292595 5 58519", "58519 139 421", "421 421 1" ]

4622120

2 2 2 5 115553

[ "4622120 2 2311060", "2311060 2 1155530", "1155530 2 577765", "577765 5 115553", "115553 115553 1" ]

4078433

607 6719

[ "4078433 607 6719", "6719 6719 1" ]

1597384

2 2 2 199673

[ "1597384 2 798692", "798692 2 399346", "399346 2 199673", "199673 199673 1" ]

3970913

89 44617

[ "3970913 89 44617", "44617 44617 1" ]

2651038

2 13 101963

[ "2651038 2 1325519", "1325519 13 101963", "101963 101963 1" ]

3506296

2 2 2 438287

[ "3506296 2 1753148", "1753148 2 876574", "876574 2 438287", "438287 438287 1" ]

4666408

2 2 2 583301

[ "4666408 2 2333204", "2333204 2 1166602", "1166602 2 583301", "583301 583301 1" ]

4654049

[ "4654049 4654049 1" ]

4337472

2 2 2 2 2 2 3 19 29 41

[ "4337472 2 2168736", "2168736 2 1084368", "1084368 2 542184", "542184 2 271092", "271092 2 135546", "135546 2 67773", "67773 3 22591", "22591 19 1189", "1189 29 41", "41 41 1" ]

1029852

2 2 3 3 28607

[ "1029852 2 514926", "514926 2 257463", "257463 3 85821", "85821 3 28607", "28607 28607 1" ]

2823281

1171 2411

[ "2823281 1171 2411", "2411 2411 1" ]

3694960

2 2 2 2 5 46187

[ "3694960 2 1847480", "1847480 2 923740", "923740 2 461870", "461870 2 230935", "230935 5 46187", "46187 46187 1" ]

1680932

2 2 11 11 23 151

[ "1680932 2 840466", "840466 2 420233", "420233 11 38203", "38203 11 3473", "3473 23 151", "151 151 1" ]

4419581

[ "4419581 4419581 1" ]

2626174

2 1313087

[ "2626174 2 1313087", "1313087 1313087 1" ]

3464274

2 3 11 52489

[ "3464274 2 1732137", "1732137 3 577379", "577379 11 52489", "52489 52489 1" ]

1123659

3 3 3 41617

[ "1123659 3 374553", "374553 3 124851", "124851 3 41617", "41617 41617 1" ]

3947038

2 1973519

[ "3947038 2 1973519", "1973519 1973519 1" ]

1538522

2 769261

[ "1538522 2 769261", "769261 769261 1" ]

3135149

1559 2011

[ "3135149 1559 2011", "2011 2011 1" ]

215098

2 13 8273

[ "215098 2 107549", "107549 13 8273", "8273 8273 1" ]

599892

2 2 3 49991

[ "599892 2 299946", "299946 2 149973", "149973 3 49991", "49991 49991 1" ]

246314

2 107 1151

[ "246314 2 123157", "123157 107 1151", "1151 1151 1" ]

289527

3 7 17 811

[ "289527 3 96509", "96509 7 13787", "13787 17 811", "811 811 1" ]

4183603

79 52957

[ "4183603 79 52957", "52957 52957 1" ]

3696163

[ "3696163 3696163 1" ]

4352159

7 19 43 761

[ "4352159 7 621737", "621737 19 32723", "32723 43 761", "761 761 1" ]

1043700

2 2 3 5 5 7 7 71

[ "1043700 2 521850", "521850 2 260925", "260925 3 86975", "86975 5 17395", "17395 5 3479", "3479 7 497", "497 7 71", "71 71 1" ]

1260092

2 2 211 1493

[ "1260092 2 630046", "630046 2 315023", "315023 211 1493", "1493 1493 1" ]

2695501

151 17851

[ "2695501 151 17851", "17851 17851 1" ]

310989

3 7 59 251

[ "310989 3 103663", "103663 7 14809", "14809 59 251", "251 251 1" ]

2055352

2 2 2 13 19763

[ "2055352 2 1027676", "1027676 2 513838", "513838 2 256919", "256919 13 19763", "19763 19763 1" ]

3593787

3 1197929

[ "3593787 3 1197929", "1197929 1197929 1" ]

4946803

[ "4946803 4946803 1" ]

2364787

61 38767

[ "2364787 61 38767", "38767 38767 1" ]