yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
3587798	2 929 1931	[ "3587798 2 1793899", "1793899 929 1931", "1931 1931 1" ]
1925158	2 109 8831	[ "1925158 2 962579", "962579 109 8831", "8831 8831 1" ]
2083529	7 7 101 421	[ "2083529 7 297647", "297647 7 42521", "42521 101 421", "421 421 1" ]
3139245	3 3 5 69761	[ "3139245 3 1046415", "1046415 3 348805", "348805 5 69761", "69761 69761 1" ]
4492553	13 345581	[ "4492553 13 345581", "345581 345581 1" ]
1399748	2 2 7 49991	[ "1399748 2 699874", "699874 2 349937", "349937 7 49991", "49991 49991 1" ]
4005759	3 107 12479	[ "4005759 3 1335253", "1335253 107 12479", "12479 12479 1" ]
2015342	2 7 143953	[ "2015342 2 1007671", "1007671 7 143953", "143953 143953 1" ]
2702280	2 2 2 3 5 7 3217	[ "2702280 2 1351140", "1351140 2 675570", "675570 2 337785", "337785 3 112595", "112595 5 22519", "22519 7 3217", "3217 3217 1" ]
4369355	5 47 18593	[ "4369355 5 873871", "873871 47 18593", "18593 18593 1" ]
1188370	2 5 151 787	[ "1188370 2 594185", "594185 5 118837", "118837 151 787", "787 787 1" ]
1114921	37 30133	[ "1114921 37 30133", "30133 30133 1" ]
1026918	2 3 3 3 3 3 2113	[ "1026918 2 513459", "513459 3 171153", "171153 3 57051", "57051 3 19017", "19017 3 6339", "6339 3 2113", "2113 2113 1" ]
515088	2 2 2 2 3 3 7 7 73	[ "515088 2 257544", "257544 2 128772", "128772 2 64386", "64386 2 32193", "32193 3 10731", "10731 3 3577", "3577 7 511", "511 7 73", "73 73 1" ]
2616059	31 84389	[ "2616059 31 84389", "84389 84389 1" ]
4793821	23 257 811	[ "4793821 23 208427", "208427 257 811", "811 811 1" ]
1774748	2 2 443687	[ "1774748 2 887374", "887374 2 443687", "443687 443687 1" ]
4469261	4469261	[ "4469261 4469261 1" ]
4921684	2 2 19 31 2089	[ "4921684 2 2460842", "2460842 2 1230421", "1230421 19 64759", "64759 31 2089", "2089 2089 1" ]
2530774	2 1265387	[ "2530774 2 1265387", "1265387 1265387 1" ]
3201606	2 3 3 3 3 19763	[ "3201606 2 1600803", "1600803 3 533601", "533601 3 177867", "177867 3 59289", "59289 3 19763", "19763 19763 1" ]
4238117	13 17 127 151	[ "4238117 13 326009", "326009 17 19177", "19177 127 151", "151 151 1" ]
1868663	1868663	[ "1868663 1868663 1" ]
508826	2 254413	[ "508826 2 254413", "254413 254413 1" ]
4473161	7 7 11 43 193	[ "4473161 7 639023", "639023 7 91289", "91289 11 8299", "8299 43 193", "193 193 1" ]
4019978	2 2009989	[ "4019978 2 2009989", "2009989 2009989 1" ]
4995581	4995581	[ "4995581 4995581 1" ]
3266938	2 277 5897	[ "3266938 2 1633469", "1633469 277 5897", "5897 5897 1" ]
1377853	1377853	[ "1377853 1377853 1" ]
4755555	3 3 5 7 31 487	[ "4755555 3 1585185", "1585185 3 528395", "528395 5 105679", "105679 7 15097", "15097 31 487", "487 487 1" ]
2266412	2 2 103 5501	[ "2266412 2 1133206", "1133206 2 566603", "566603 103 5501", "5501 5501 1" ]
3779582	2 31 60961	[ "3779582 2 1889791", "1889791 31 60961", "60961 60961 1" ]
1939235	5 19 137 149	[ "1939235 5 387847", "387847 19 20413", "20413 137 149", "149 149 1" ]
2532003	3 844001	[ "2532003 3 844001", "844001 844001 1" ]
539517	3 11 16349	[ "539517 3 179839", "179839 11 16349", "16349 16349 1" ]
2818393	2818393	[ "2818393 2818393 1" ]
3326245	5 13 73 701	[ "3326245 5 665249", "665249 13 51173", "51173 73 701", "701 701 1" ]
71998	2 35999	[ "71998 2 35999", "35999 35999 1" ]
3687643	197 18719	[ "3687643 197 18719", "18719 18719 1" ]
277048	2 2 2 34631	[ "277048 2 138524", "138524 2 69262", "69262 2 34631", "34631 34631 1" ]
3852360	2 2 2 3 3 3 3 5 29 41	[ "3852360 2 1926180", "1926180 2 963090", "963090 2 481545", "481545 3 160515", "160515 3 53505", "53505 3 17835", "17835 3 5945", "5945 5 1189", "1189 29 41", "41 41 1" ]
1743176	2 2 2 193 1129	[ "1743176 2 871588", "871588 2 435794", "435794 2 217897", "217897 193 1129", "1129 1129 1" ]
2179788	2 2 3 13 89 157	[ "2179788 2 1089894", "1089894 2 544947", "544947 3 181649", "181649 13 13973", "13973 89 157", "157 157 1" ]
1873139	29 64591	[ "1873139 29 64591", "64591 64591 1" ]
3440034	2 3 3 13 61 241	[ "3440034 2 1720017", "1720017 3 573339", "573339 3 191113", "191113 13 14701", "14701 61 241", "241 241 1" ]
4336138	2 29 74761	[ "4336138 2 2168069", "2168069 29 74761", "74761 74761 1" ]
3133617	3 233 4483	[ "3133617 3 1044539", "1044539 233 4483", "4483 4483 1" ]
1780191	3 3 3 7 9419	[ "1780191 3 593397", "593397 3 197799", "197799 3 65933", "65933 7 9419", "9419 9419 1" ]
290546	2 53 2741	[ "290546 2 145273", "145273 53 2741", "2741 2741 1" ]
342296	2 2 2 42787	[ "342296 2 171148", "171148 2 85574", "85574 2 42787", "42787 42787 1" ]
1532862	2 3 3 85159	[ "1532862 2 766431", "766431 3 255477", "255477 3 85159", "85159 85159 1" ]
273546	2 3 3 7 13 167	[ "273546 2 136773", "136773 3 45591", "45591 3 15197", "15197 7 2171", "2171 13 167", "167 167 1" ]
1687834	2 433 1949	[ "1687834 2 843917", "843917 433 1949", "1949 1949 1" ]
4211340	2 2 3 5 7 37 271	[ "4211340 2 2105670", "2105670 2 1052835", "1052835 3 350945", "350945 5 70189", "70189 7 10027", "10027 37 271", "271 271 1" ]
888202	2 7 63443	[ "888202 2 444101", "444101 7 63443", "63443 63443 1" ]
3280706	2 11 13 11471	[ "3280706 2 1640353", "1640353 11 149123", "149123 13 11471", "11471 11471 1" ]
479819	257 1867	[ "479819 257 1867", "1867 1867 1" ]
1592698	2 131 6079	[ "1592698 2 796349", "796349 131 6079", "6079 6079 1" ]
1992241	1992241	[ "1992241 1992241 1" ]
3693881	3693881	[ "3693881 3693881 1" ]
2651813	17 389 401	[ "2651813 17 155989", "155989 389 401", "401 401 1" ]
2589446	2 1294723	[ "2589446 2 1294723", "1294723 1294723 1" ]
3211782	2 3 7 76471	[ "3211782 2 1605891", "1605891 3 535297", "535297 7 76471", "76471 76471 1" ]
92896	2 2 2 2 2 2903	[ "92896 2 46448", "46448 2 23224", "23224 2 11612", "11612 2 5806", "5806 2 2903", "2903 2903 1" ]
4891975	5 5 11 17789	[ "4891975 5 978395", "978395 5 195679", "195679 11 17789", "17789 17789 1" ]
3023364	2 2 3 251947	[ "3023364 2 1511682", "1511682 2 755841", "755841 3 251947", "251947 251947 1" ]
4481603	7 640229	[ "4481603 7 640229", "640229 640229 1" ]
2831657	2831657	[ "2831657 2831657 1" ]
4813328	2 2 2 2 13 73 317	[ "4813328 2 2406664", "2406664 2 1203332", "1203332 2 601666", "601666 2 300833", "300833 13 23141", "23141 73 317", "317 317 1" ]
3834394	2 1917197	[ "3834394 2 1917197", "1917197 1917197 1" ]
2775505	5 17 32653	[ "2775505 5 555101", "555101 17 32653", "32653 32653 1" ]
4284645	3 5 285643	[ "4284645 3 1428215", "1428215 5 285643", "285643 285643 1" ]
2214228	2 2 3 37 4987	[ "2214228 2 1107114", "1107114 2 553557", "553557 3 184519", "184519 37 4987", "4987 4987 1" ]
3031962	2 3 505327	[ "3031962 2 1515981", "1515981 3 505327", "505327 505327 1" ]
4571726	2 2285863	[ "4571726 2 2285863", "2285863 2285863 1" ]
4717624	2 2 2 19 41 757	[ "4717624 2 2358812", "2358812 2 1179406", "1179406 2 589703", "589703 19 31037", "31037 41 757", "757 757 1" ]
1405355	5 7 40153	[ "1405355 5 281071", "281071 7 40153", "40153 40153 1" ]
4855628	2 2 1213907	[ "4855628 2 2427814", "2427814 2 1213907", "1213907 1213907 1" ]
4689367	379 12373	[ "4689367 379 12373", "12373 12373 1" ]
2594818	2 61 21269	[ "2594818 2 1297409", "1297409 61 21269", "21269 21269 1" ]
1101457	7 157351	[ "1101457 7 157351", "157351 157351 1" ]
3239379	3 3 3 11 13 839	[ "3239379 3 1079793", "1079793 3 359931", "359931 3 119977", "119977 11 10907", "10907 13 839", "839 839 1" ]
3723167	7 7 75983	[ "3723167 7 531881", "531881 7 75983", "75983 75983 1" ]
548200	2 2 2 5 5 2741	[ "548200 2 274100", "274100 2 137050", "137050 2 68525", "68525 5 13705", "13705 5 2741", "2741 2741 1" ]
92561	7 7 1889	[ "92561 7 13223", "13223 7 1889", "1889 1889 1" ]
3370003	7 13 29 1277	[ "3370003 7 481429", "481429 13 37033", "37033 29 1277", "1277 1277 1" ]
4160602	2 337 6173	[ "4160602 2 2080301", "2080301 337 6173", "6173 6173 1" ]
1672358	2 17 101 487	[ "1672358 2 836179", "836179 17 49187", "49187 101 487", "487 487 1" ]
2558093	2558093	[ "2558093 2558093 1" ]
4207841	11 61 6271	[ "4207841 11 382531", "382531 61 6271", "6271 6271 1" ]
4847797	223 21739	[ "4847797 223 21739", "21739 21739 1" ]
4646803	7 127 5227	[ "4646803 7 663829", "663829 127 5227", "5227 5227 1" ]
4687110	2 3 3 5 19 2741	[ "4687110 2 2343555", "2343555 3 781185", "781185 3 260395", "260395 5 52079", "52079 19 2741", "2741 2741 1" ]
1746229	23 23 3301	[ "1746229 23 75923", "75923 23 3301", "3301 3301 1" ]
1673273	7 19 23 547	[ "1673273 7 239039", "239039 19 12581", "12581 23 547", "547 547 1" ]
163447	73 2239	[ "163447 73 2239", "2239 2239 1" ]
4209973	1117 3769	[ "4209973 1117 3769", "3769 3769 1" ]
3277099	7 468157	[ "3277099 7 468157", "468157 468157 1" ]
652913	652913	[ "652913 652913 1" ]
1846168	2 2 2 230771	[ "1846168 2 923084", "923084 2 461542", "461542 2 230771", "230771 230771 1" ]

3587798

2 929 1931

[ "3587798 2 1793899", "1793899 929 1931", "1931 1931 1" ]

1925158

2 109 8831

[ "1925158 2 962579", "962579 109 8831", "8831 8831 1" ]

2083529

7 7 101 421

[ "2083529 7 297647", "297647 7 42521", "42521 101 421", "421 421 1" ]

3139245

3 3 5 69761

[ "3139245 3 1046415", "1046415 3 348805", "348805 5 69761", "69761 69761 1" ]

4492553

13 345581

[ "4492553 13 345581", "345581 345581 1" ]

1399748

2 2 7 49991

[ "1399748 2 699874", "699874 2 349937", "349937 7 49991", "49991 49991 1" ]

4005759

3 107 12479

[ "4005759 3 1335253", "1335253 107 12479", "12479 12479 1" ]

2015342

2 7 143953

[ "2015342 2 1007671", "1007671 7 143953", "143953 143953 1" ]

2702280

2 2 2 3 5 7 3217

[ "2702280 2 1351140", "1351140 2 675570", "675570 2 337785", "337785 3 112595", "112595 5 22519", "22519 7 3217", "3217 3217 1" ]

4369355

5 47 18593

[ "4369355 5 873871", "873871 47 18593", "18593 18593 1" ]

1188370

2 5 151 787

[ "1188370 2 594185", "594185 5 118837", "118837 151 787", "787 787 1" ]

1114921

37 30133

[ "1114921 37 30133", "30133 30133 1" ]

1026918

2 3 3 3 3 3 2113

[ "1026918 2 513459", "513459 3 171153", "171153 3 57051", "57051 3 19017", "19017 3 6339", "6339 3 2113", "2113 2113 1" ]

515088

2 2 2 2 3 3 7 7 73

[ "515088 2 257544", "257544 2 128772", "128772 2 64386", "64386 2 32193", "32193 3 10731", "10731 3 3577", "3577 7 511", "511 7 73", "73 73 1" ]

2616059

31 84389

[ "2616059 31 84389", "84389 84389 1" ]

4793821

23 257 811

[ "4793821 23 208427", "208427 257 811", "811 811 1" ]

1774748

2 2 443687

[ "1774748 2 887374", "887374 2 443687", "443687 443687 1" ]

4469261

[ "4469261 4469261 1" ]

4921684

2 2 19 31 2089

[ "4921684 2 2460842", "2460842 2 1230421", "1230421 19 64759", "64759 31 2089", "2089 2089 1" ]

2530774

2 1265387

[ "2530774 2 1265387", "1265387 1265387 1" ]

3201606

2 3 3 3 3 19763

[ "3201606 2 1600803", "1600803 3 533601", "533601 3 177867", "177867 3 59289", "59289 3 19763", "19763 19763 1" ]

4238117

13 17 127 151

[ "4238117 13 326009", "326009 17 19177", "19177 127 151", "151 151 1" ]

1868663

[ "1868663 1868663 1" ]

508826

2 254413

[ "508826 2 254413", "254413 254413 1" ]

4473161

7 7 11 43 193

[ "4473161 7 639023", "639023 7 91289", "91289 11 8299", "8299 43 193", "193 193 1" ]

4019978

2 2009989

[ "4019978 2 2009989", "2009989 2009989 1" ]

4995581

[ "4995581 4995581 1" ]

3266938

2 277 5897

[ "3266938 2 1633469", "1633469 277 5897", "5897 5897 1" ]

1377853

[ "1377853 1377853 1" ]

4755555

3 3 5 7 31 487

[ "4755555 3 1585185", "1585185 3 528395", "528395 5 105679", "105679 7 15097", "15097 31 487", "487 487 1" ]

2266412

2 2 103 5501

[ "2266412 2 1133206", "1133206 2 566603", "566603 103 5501", "5501 5501 1" ]

3779582

2 31 60961

[ "3779582 2 1889791", "1889791 31 60961", "60961 60961 1" ]

1939235

5 19 137 149

[ "1939235 5 387847", "387847 19 20413", "20413 137 149", "149 149 1" ]

2532003

3 844001

[ "2532003 3 844001", "844001 844001 1" ]

539517

3 11 16349

[ "539517 3 179839", "179839 11 16349", "16349 16349 1" ]

2818393

[ "2818393 2818393 1" ]

3326245

5 13 73 701

[ "3326245 5 665249", "665249 13 51173", "51173 73 701", "701 701 1" ]

71998

2 35999

[ "71998 2 35999", "35999 35999 1" ]

3687643

197 18719

[ "3687643 197 18719", "18719 18719 1" ]

277048

2 2 2 34631

[ "277048 2 138524", "138524 2 69262", "69262 2 34631", "34631 34631 1" ]

3852360

2 2 2 3 3 3 3 5 29 41

[ "3852360 2 1926180", "1926180 2 963090", "963090 2 481545", "481545 3 160515", "160515 3 53505", "53505 3 17835", "17835 3 5945", "5945 5 1189", "1189 29 41", "41 41 1" ]

1743176

2 2 2 193 1129

[ "1743176 2 871588", "871588 2 435794", "435794 2 217897", "217897 193 1129", "1129 1129 1" ]

2179788

2 2 3 13 89 157

[ "2179788 2 1089894", "1089894 2 544947", "544947 3 181649", "181649 13 13973", "13973 89 157", "157 157 1" ]

1873139

29 64591

[ "1873139 29 64591", "64591 64591 1" ]

3440034

2 3 3 13 61 241

[ "3440034 2 1720017", "1720017 3 573339", "573339 3 191113", "191113 13 14701", "14701 61 241", "241 241 1" ]

4336138

2 29 74761

[ "4336138 2 2168069", "2168069 29 74761", "74761 74761 1" ]

3133617

3 233 4483

[ "3133617 3 1044539", "1044539 233 4483", "4483 4483 1" ]

1780191

3 3 3 7 9419

[ "1780191 3 593397", "593397 3 197799", "197799 3 65933", "65933 7 9419", "9419 9419 1" ]

290546

2 53 2741

[ "290546 2 145273", "145273 53 2741", "2741 2741 1" ]

342296

2 2 2 42787

[ "342296 2 171148", "171148 2 85574", "85574 2 42787", "42787 42787 1" ]

1532862

2 3 3 85159

[ "1532862 2 766431", "766431 3 255477", "255477 3 85159", "85159 85159 1" ]

273546

2 3 3 7 13 167

[ "273546 2 136773", "136773 3 45591", "45591 3 15197", "15197 7 2171", "2171 13 167", "167 167 1" ]

1687834

2 433 1949

[ "1687834 2 843917", "843917 433 1949", "1949 1949 1" ]

4211340

2 2 3 5 7 37 271

[ "4211340 2 2105670", "2105670 2 1052835", "1052835 3 350945", "350945 5 70189", "70189 7 10027", "10027 37 271", "271 271 1" ]

888202

2 7 63443

[ "888202 2 444101", "444101 7 63443", "63443 63443 1" ]

3280706

2 11 13 11471

[ "3280706 2 1640353", "1640353 11 149123", "149123 13 11471", "11471 11471 1" ]

479819

257 1867

[ "479819 257 1867", "1867 1867 1" ]

1592698

2 131 6079

[ "1592698 2 796349", "796349 131 6079", "6079 6079 1" ]

1992241

[ "1992241 1992241 1" ]

3693881

[ "3693881 3693881 1" ]

2651813

17 389 401

[ "2651813 17 155989", "155989 389 401", "401 401 1" ]

2589446

2 1294723

[ "2589446 2 1294723", "1294723 1294723 1" ]

3211782

2 3 7 76471

[ "3211782 2 1605891", "1605891 3 535297", "535297 7 76471", "76471 76471 1" ]

92896

2 2 2 2 2 2903

[ "92896 2 46448", "46448 2 23224", "23224 2 11612", "11612 2 5806", "5806 2 2903", "2903 2903 1" ]

4891975

5 5 11 17789

[ "4891975 5 978395", "978395 5 195679", "195679 11 17789", "17789 17789 1" ]

3023364

2 2 3 251947

[ "3023364 2 1511682", "1511682 2 755841", "755841 3 251947", "251947 251947 1" ]

4481603

7 640229

[ "4481603 7 640229", "640229 640229 1" ]

2831657

[ "2831657 2831657 1" ]

4813328

2 2 2 2 13 73 317

[ "4813328 2 2406664", "2406664 2 1203332", "1203332 2 601666", "601666 2 300833", "300833 13 23141", "23141 73 317", "317 317 1" ]

3834394

2 1917197

[ "3834394 2 1917197", "1917197 1917197 1" ]

2775505

5 17 32653

[ "2775505 5 555101", "555101 17 32653", "32653 32653 1" ]

4284645

3 5 285643

[ "4284645 3 1428215", "1428215 5 285643", "285643 285643 1" ]

2214228

2 2 3 37 4987

[ "2214228 2 1107114", "1107114 2 553557", "553557 3 184519", "184519 37 4987", "4987 4987 1" ]

3031962

2 3 505327

[ "3031962 2 1515981", "1515981 3 505327", "505327 505327 1" ]

4571726

2 2285863

[ "4571726 2 2285863", "2285863 2285863 1" ]

4717624

2 2 2 19 41 757

[ "4717624 2 2358812", "2358812 2 1179406", "1179406 2 589703", "589703 19 31037", "31037 41 757", "757 757 1" ]

1405355

5 7 40153

[ "1405355 5 281071", "281071 7 40153", "40153 40153 1" ]

4855628

2 2 1213907

[ "4855628 2 2427814", "2427814 2 1213907", "1213907 1213907 1" ]

4689367

379 12373

[ "4689367 379 12373", "12373 12373 1" ]

2594818

2 61 21269

[ "2594818 2 1297409", "1297409 61 21269", "21269 21269 1" ]

1101457

7 157351

[ "1101457 7 157351", "157351 157351 1" ]

3239379

3 3 3 11 13 839

[ "3239379 3 1079793", "1079793 3 359931", "359931 3 119977", "119977 11 10907", "10907 13 839", "839 839 1" ]

3723167

7 7 75983

[ "3723167 7 531881", "531881 7 75983", "75983 75983 1" ]

548200

2 2 2 5 5 2741

[ "548200 2 274100", "274100 2 137050", "137050 2 68525", "68525 5 13705", "13705 5 2741", "2741 2741 1" ]

92561

7 7 1889

[ "92561 7 13223", "13223 7 1889", "1889 1889 1" ]

3370003

7 13 29 1277

[ "3370003 7 481429", "481429 13 37033", "37033 29 1277", "1277 1277 1" ]

4160602

2 337 6173

[ "4160602 2 2080301", "2080301 337 6173", "6173 6173 1" ]

1672358

2 17 101 487

[ "1672358 2 836179", "836179 17 49187", "49187 101 487", "487 487 1" ]

2558093

[ "2558093 2558093 1" ]

4207841

11 61 6271

[ "4207841 11 382531", "382531 61 6271", "6271 6271 1" ]

4847797

223 21739

[ "4847797 223 21739", "21739 21739 1" ]

4646803

7 127 5227

[ "4646803 7 663829", "663829 127 5227", "5227 5227 1" ]

4687110

2 3 3 5 19 2741

[ "4687110 2 2343555", "2343555 3 781185", "781185 3 260395", "260395 5 52079", "52079 19 2741", "2741 2741 1" ]

1746229

23 23 3301

[ "1746229 23 75923", "75923 23 3301", "3301 3301 1" ]

1673273

7 19 23 547

[ "1673273 7 239039", "239039 19 12581", "12581 23 547", "547 547 1" ]

163447

73 2239

[ "163447 73 2239", "2239 2239 1" ]

4209973

1117 3769

[ "4209973 1117 3769", "3769 3769 1" ]

3277099

7 468157

[ "3277099 7 468157", "468157 468157 1" ]

652913

[ "652913 652913 1" ]

1846168

2 2 2 230771

[ "1846168 2 923084", "923084 2 461542", "461542 2 230771", "230771 230771 1" ]