yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
4485684	2 2 3 7 53401	[ "4485684 2 2242842", "2242842 2 1121421", "1121421 3 373807", "373807 7 53401", "53401 53401 1" ]
3036919	3036919	[ "3036919 3036919 1" ]
707752	2 2 2 88469	[ "707752 2 353876", "353876 2 176938", "176938 2 88469", "88469 88469 1" ]
332309	332309	[ "332309 332309 1" ]
2007013	2007013	[ "2007013 2007013 1" ]
3668547	3 227 5387	[ "3668547 3 1222849", "1222849 227 5387", "5387 5387 1" ]
2161378	2 751 1439	[ "2161378 2 1080689", "1080689 751 1439", "1439 1439 1" ]
798958	2 83 4813	[ "798958 2 399479", "399479 83 4813", "4813 4813 1" ]
4671913	4671913	[ "4671913 4671913 1" ]
3557773	3557773	[ "3557773 3557773 1" ]
419326	2 71 2953	[ "419326 2 209663", "209663 71 2953", "2953 2953 1" ]
271924	2 2 157 433	[ "271924 2 135962", "135962 2 67981", "67981 157 433", "433 433 1" ]
4772006	2 2386003	[ "4772006 2 2386003", "2386003 2386003 1" ]
2680812	2 2 3 3 113 659	[ "2680812 2 1340406", "1340406 2 670203", "670203 3 223401", "223401 3 74467", "74467 113 659", "659 659 1" ]
4494253	577 7789	[ "4494253 577 7789", "7789 7789 1" ]
570351	3 41 4637	[ "570351 3 190117", "190117 41 4637", "4637 4637 1" ]
1494387	3 3 166043	[ "1494387 3 498129", "498129 3 166043", "166043 166043 1" ]
4892369	4892369	[ "4892369 4892369 1" ]
3502555	5 7 19 23 229	[ "3502555 5 700511", "700511 7 100073", "100073 19 5267", "5267 23 229", "229 229 1" ]
1611981	3 3 3 3 7 2843	[ "1611981 3 537327", "537327 3 179109", "179109 3 59703", "59703 3 19901", "19901 7 2843", "2843 2843 1" ]
261531	3 3 29059	[ "261531 3 87177", "87177 3 29059", "29059 29059 1" ]
693625	5 5 5 31 179	[ "693625 5 138725", "138725 5 27745", "27745 5 5549", "5549 31 179", "179 179 1" ]
3333112	2 2 2 401 1039	[ "3333112 2 1666556", "1666556 2 833278", "833278 2 416639", "416639 401 1039", "1039 1039 1" ]
438852	2 2 3 36571	[ "438852 2 219426", "219426 2 109713", "109713 3 36571", "36571 36571 1" ]
2318131	127 18253	[ "2318131 127 18253", "18253 18253 1" ]
4853010	2 3 5 83 1949	[ "4853010 2 2426505", "2426505 3 808835", "808835 5 161767", "161767 83 1949", "1949 1949 1" ]
2327527	2327527	[ "2327527 2327527 1" ]
3116786	2 601 2593	[ "3116786 2 1558393", "1558393 601 2593", "2593 2593 1" ]
2858410	2 5 285841	[ "2858410 2 1429205", "1429205 5 285841", "285841 285841 1" ]
4029940	2 2 5 201497	[ "4029940 2 2014970", "2014970 2 1007485", "1007485 5 201497", "201497 201497 1" ]
3626236	2 2 17 53327	[ "3626236 2 1813118", "1813118 2 906559", "906559 17 53327", "53327 53327 1" ]
4261107	3 1420369	[ "4261107 3 1420369", "1420369 1420369 1" ]
4618832	2 2 2 2 17 16981	[ "4618832 2 2309416", "2309416 2 1154708", "1154708 2 577354", "577354 2 288677", "288677 17 16981", "16981 16981 1" ]
3607385	5 41 17597	[ "3607385 5 721477", "721477 41 17597", "17597 17597 1" ]
3789916	2 2 13 72883	[ "3789916 2 1894958", "1894958 2 947479", "947479 13 72883", "72883 72883 1" ]
4805003	7 461 1489	[ "4805003 7 686429", "686429 461 1489", "1489 1489 1" ]
1646463	3 7 13 37 163	[ "1646463 3 548821", "548821 7 78403", "78403 13 6031", "6031 37 163", "163 163 1" ]
4586233	31 337 439	[ "4586233 31 147943", "147943 337 439", "439 439 1" ]
1573416	2 2 2 3 3 13 41 41	[ "1573416 2 786708", "786708 2 393354", "393354 2 196677", "196677 3 65559", "65559 3 21853", "21853 13 1681", "1681 41 41", "41 41 1" ]
989342	2 494671	[ "989342 2 494671", "494671 494671 1" ]
2192751	3 3 3 3 11 23 107	[ "2192751 3 730917", "730917 3 243639", "243639 3 81213", "81213 3 27071", "27071 11 2461", "2461 23 107", "107 107 1" ]
3957356	2 2 13 76103	[ "3957356 2 1978678", "1978678 2 989339", "989339 13 76103", "76103 76103 1" ]
4056624	2 2 2 2 3 3 11 13 197	[ "4056624 2 2028312", "2028312 2 1014156", "1014156 2 507078", "507078 2 253539", "253539 3 84513", "84513 3 28171", "28171 11 2561", "2561 13 197", "197 197 1" ]
452821	452821	[ "452821 452821 1" ]
3422913	3 13 87767	[ "3422913 3 1140971", "1140971 13 87767", "87767 87767 1" ]
639633	3 101 2111	[ "639633 3 213211", "213211 101 2111", "2111 2111 1" ]
3190085	5 101 6317	[ "3190085 5 638017", "638017 101 6317", "6317 6317 1" ]
3716381	19 195599	[ "3716381 19 195599", "195599 195599 1" ]
599527	661 907	[ "599527 661 907", "907 907 1" ]
3007094	2 67 22441	[ "3007094 2 1503547", "1503547 67 22441", "22441 22441 1" ]
96415	5 11 1753	[ "96415 5 19283", "19283 11 1753", "1753 1753 1" ]
3819863	23 166081	[ "3819863 23 166081", "166081 166081 1" ]
4557007	7 13 50077	[ "4557007 7 651001", "651001 13 50077", "50077 50077 1" ]
2547883	13 195991	[ "2547883 13 195991", "195991 195991 1" ]
3273232	2 2 2 2 149 1373	[ "3273232 2 1636616", "1636616 2 818308", "818308 2 409154", "409154 2 204577", "204577 149 1373", "1373 1373 1" ]
768407	23 33409	[ "768407 23 33409", "33409 33409 1" ]
3856186	2 1928093	[ "3856186 2 1928093", "1928093 1928093 1" ]
3853865	5 19 113 359	[ "3853865 5 770773", "770773 19 40567", "40567 113 359", "359 359 1" ]
946727	946727	[ "946727 946727 1" ]
765655	5 11 13921	[ "765655 5 153131", "153131 11 13921", "13921 13921 1" ]
817782	2 3 7 19471	[ "817782 2 408891", "408891 3 136297", "136297 7 19471", "19471 19471 1" ]
1914898	2 37 113 229	[ "1914898 2 957449", "957449 37 25877", "25877 113 229", "229 229 1" ]
4620833	7 660119	[ "4620833 7 660119", "660119 660119 1" ]
2143341	3 3 3 3 47 563	[ "2143341 3 714447", "714447 3 238149", "238149 3 79383", "79383 3 26461", "26461 47 563", "563 563 1" ]
2480314	2 71 17467	[ "2480314 2 1240157", "1240157 71 17467", "17467 17467 1" ]
557966	2 227 1229	[ "557966 2 278983", "278983 227 1229", "1229 1229 1" ]
1793157	3 29 20611	[ "1793157 3 597719", "597719 29 20611", "20611 20611 1" ]
464816	2 2 2 2 11 19 139	[ "464816 2 232408", "232408 2 116204", "116204 2 58102", "58102 2 29051", "29051 11 2641", "2641 19 139", "139 139 1" ]
4992638	2 7 227 1571	[ "4992638 2 2496319", "2496319 7 356617", "356617 227 1571", "1571 1571 1" ]
334921	29 11549	[ "334921 29 11549", "11549 11549 1" ]
951802	2 67 7103	[ "951802 2 475901", "475901 67 7103", "7103 7103 1" ]
786857	29 43 631	[ "786857 29 27133", "27133 43 631", "631 631 1" ]
518201	29 107 167	[ "518201 29 17869", "17869 107 167", "167 167 1" ]
839941	571 1471	[ "839941 571 1471", "1471 1471 1" ]
4469963	17 17 15467	[ "4469963 17 262939", "262939 17 15467", "15467 15467 1" ]
4787303	617 7759	[ "4787303 617 7759", "7759 7759 1" ]
3623129	19 41 4651	[ "3623129 19 190691", "190691 41 4651", "4651 4651 1" ]
3696920	2 2 2 5 29 3187	[ "3696920 2 1848460", "1848460 2 924230", "924230 2 462115", "462115 5 92423", "92423 29 3187", "3187 3187 1" ]
3624038	2 11 164729	[ "3624038 2 1812019", "1812019 11 164729", "164729 164729 1" ]
4206977	547 7691	[ "4206977 547 7691", "7691 7691 1" ]
4719975	3 5 5 13 47 103	[ "4719975 3 1573325", "1573325 5 314665", "314665 5 62933", "62933 13 4841", "4841 47 103", "103 103 1" ]
1513733	13 13 13 13 53	[ "1513733 13 116441", "116441 13 8957", "8957 13 689", "689 13 53", "53 53 1" ]
2524079	59 179 239	[ "2524079 59 42781", "42781 179 239", "239 239 1" ]
3833120	2 2 2 2 2 5 23957	[ "3833120 2 1916560", "1916560 2 958280", "958280 2 479140", "479140 2 239570", "239570 2 119785", "119785 5 23957", "23957 23957 1" ]
1085948	2 2 73 3719	[ "1085948 2 542974", "542974 2 271487", "271487 73 3719", "3719 3719 1" ]
421055	5 84211	[ "421055 5 84211", "84211 84211 1" ]
4117181	4117181	[ "4117181 4117181 1" ]
460307	41 103 109	[ "460307 41 11227", "11227 103 109", "109 109 1" ]
617492	2 2 154373	[ "617492 2 308746", "308746 2 154373", "154373 154373 1" ]
500203	11 37 1229	[ "500203 11 45473", "45473 37 1229", "1229 1229 1" ]
3598600	2 2 2 5 5 19 947	[ "3598600 2 1799300", "1799300 2 899650", "899650 2 449825", "449825 5 89965", "89965 5 17993", "17993 19 947", "947 947 1" ]
4698576	2 2 2 2 3 3 67 487	[ "4698576 2 2349288", "2349288 2 1174644", "1174644 2 587322", "587322 2 293661", "293661 3 97887", "97887 3 32629", "32629 67 487", "487 487 1" ]
3565567	3565567	[ "3565567 3565567 1" ]
4425792	2 2 2 2 2 2 3 7 37 89	[ "4425792 2 2212896", "2212896 2 1106448", "1106448 2 553224", "553224 2 276612", "276612 2 138306", "138306 2 69153", "69153 3 23051", "23051 7 3293", "3293 37 89", "89 89 1" ]
1043945	5 7 7 4261	[ "1043945 5 208789", "208789 7 29827", "29827 7 4261", "4261 4261 1" ]
3782047	227 16661	[ "3782047 227 16661", "16661 16661 1" ]
152574	2 3 59 431	[ "152574 2 76287", "76287 3 25429", "25429 59 431", "431 431 1" ]
3174048	2 2 2 2 2 3 3 103 107	[ "3174048 2 1587024", "1587024 2 793512", "793512 2 396756", "396756 2 198378", "198378 2 99189", "99189 3 33063", "33063 3 11021", "11021 103 107", "107 107 1" ]
1818926	2 909463	[ "1818926 2 909463", "909463 909463 1" ]
2836346	2 37 38329	[ "2836346 2 1418173", "1418173 37 38329", "38329 38329 1" ]

4485684

2 2 3 7 53401

[ "4485684 2 2242842", "2242842 2 1121421", "1121421 3 373807", "373807 7 53401", "53401 53401 1" ]

3036919

[ "3036919 3036919 1" ]

707752

2 2 2 88469

[ "707752 2 353876", "353876 2 176938", "176938 2 88469", "88469 88469 1" ]

332309

[ "332309 332309 1" ]

2007013

[ "2007013 2007013 1" ]

3668547

3 227 5387

[ "3668547 3 1222849", "1222849 227 5387", "5387 5387 1" ]

2161378

2 751 1439

[ "2161378 2 1080689", "1080689 751 1439", "1439 1439 1" ]

798958

2 83 4813

[ "798958 2 399479", "399479 83 4813", "4813 4813 1" ]

4671913

[ "4671913 4671913 1" ]

3557773

[ "3557773 3557773 1" ]

419326

2 71 2953

[ "419326 2 209663", "209663 71 2953", "2953 2953 1" ]

271924

2 2 157 433

[ "271924 2 135962", "135962 2 67981", "67981 157 433", "433 433 1" ]

4772006

2 2386003

[ "4772006 2 2386003", "2386003 2386003 1" ]

2680812

2 2 3 3 113 659

[ "2680812 2 1340406", "1340406 2 670203", "670203 3 223401", "223401 3 74467", "74467 113 659", "659 659 1" ]

4494253

577 7789

[ "4494253 577 7789", "7789 7789 1" ]

570351

3 41 4637

[ "570351 3 190117", "190117 41 4637", "4637 4637 1" ]

1494387

3 3 166043

[ "1494387 3 498129", "498129 3 166043", "166043 166043 1" ]

4892369

[ "4892369 4892369 1" ]

3502555

5 7 19 23 229

[ "3502555 5 700511", "700511 7 100073", "100073 19 5267", "5267 23 229", "229 229 1" ]

1611981

3 3 3 3 7 2843

[ "1611981 3 537327", "537327 3 179109", "179109 3 59703", "59703 3 19901", "19901 7 2843", "2843 2843 1" ]

261531

3 3 29059

[ "261531 3 87177", "87177 3 29059", "29059 29059 1" ]

693625

5 5 5 31 179

[ "693625 5 138725", "138725 5 27745", "27745 5 5549", "5549 31 179", "179 179 1" ]

3333112

2 2 2 401 1039

[ "3333112 2 1666556", "1666556 2 833278", "833278 2 416639", "416639 401 1039", "1039 1039 1" ]

438852

2 2 3 36571

[ "438852 2 219426", "219426 2 109713", "109713 3 36571", "36571 36571 1" ]

2318131

127 18253

[ "2318131 127 18253", "18253 18253 1" ]

4853010

2 3 5 83 1949

[ "4853010 2 2426505", "2426505 3 808835", "808835 5 161767", "161767 83 1949", "1949 1949 1" ]

2327527

[ "2327527 2327527 1" ]

3116786

2 601 2593

[ "3116786 2 1558393", "1558393 601 2593", "2593 2593 1" ]

2858410

2 5 285841

[ "2858410 2 1429205", "1429205 5 285841", "285841 285841 1" ]

4029940

2 2 5 201497

[ "4029940 2 2014970", "2014970 2 1007485", "1007485 5 201497", "201497 201497 1" ]

3626236

2 2 17 53327

[ "3626236 2 1813118", "1813118 2 906559", "906559 17 53327", "53327 53327 1" ]

4261107

3 1420369

[ "4261107 3 1420369", "1420369 1420369 1" ]

4618832

2 2 2 2 17 16981

[ "4618832 2 2309416", "2309416 2 1154708", "1154708 2 577354", "577354 2 288677", "288677 17 16981", "16981 16981 1" ]

3607385

5 41 17597

[ "3607385 5 721477", "721477 41 17597", "17597 17597 1" ]

3789916

2 2 13 72883

[ "3789916 2 1894958", "1894958 2 947479", "947479 13 72883", "72883 72883 1" ]

4805003

7 461 1489

[ "4805003 7 686429", "686429 461 1489", "1489 1489 1" ]

1646463

3 7 13 37 163

[ "1646463 3 548821", "548821 7 78403", "78403 13 6031", "6031 37 163", "163 163 1" ]

4586233

31 337 439

[ "4586233 31 147943", "147943 337 439", "439 439 1" ]

1573416

2 2 2 3 3 13 41 41

[ "1573416 2 786708", "786708 2 393354", "393354 2 196677", "196677 3 65559", "65559 3 21853", "21853 13 1681", "1681 41 41", "41 41 1" ]

989342

2 494671

[ "989342 2 494671", "494671 494671 1" ]

2192751

3 3 3 3 11 23 107

[ "2192751 3 730917", "730917 3 243639", "243639 3 81213", "81213 3 27071", "27071 11 2461", "2461 23 107", "107 107 1" ]

3957356

2 2 13 76103

[ "3957356 2 1978678", "1978678 2 989339", "989339 13 76103", "76103 76103 1" ]

4056624

2 2 2 2 3 3 11 13 197

[ "4056624 2 2028312", "2028312 2 1014156", "1014156 2 507078", "507078 2 253539", "253539 3 84513", "84513 3 28171", "28171 11 2561", "2561 13 197", "197 197 1" ]

452821

[ "452821 452821 1" ]

3422913

3 13 87767

[ "3422913 3 1140971", "1140971 13 87767", "87767 87767 1" ]

639633

3 101 2111

[ "639633 3 213211", "213211 101 2111", "2111 2111 1" ]

3190085

5 101 6317

[ "3190085 5 638017", "638017 101 6317", "6317 6317 1" ]

3716381

19 195599

[ "3716381 19 195599", "195599 195599 1" ]

599527

661 907

[ "599527 661 907", "907 907 1" ]

3007094

2 67 22441

[ "3007094 2 1503547", "1503547 67 22441", "22441 22441 1" ]

96415

5 11 1753

[ "96415 5 19283", "19283 11 1753", "1753 1753 1" ]

3819863

23 166081

[ "3819863 23 166081", "166081 166081 1" ]

4557007

7 13 50077

[ "4557007 7 651001", "651001 13 50077", "50077 50077 1" ]

2547883

13 195991

[ "2547883 13 195991", "195991 195991 1" ]

3273232

2 2 2 2 149 1373

[ "3273232 2 1636616", "1636616 2 818308", "818308 2 409154", "409154 2 204577", "204577 149 1373", "1373 1373 1" ]

768407

23 33409

[ "768407 23 33409", "33409 33409 1" ]

3856186

2 1928093

[ "3856186 2 1928093", "1928093 1928093 1" ]

3853865

5 19 113 359

[ "3853865 5 770773", "770773 19 40567", "40567 113 359", "359 359 1" ]

946727

[ "946727 946727 1" ]

765655

5 11 13921

[ "765655 5 153131", "153131 11 13921", "13921 13921 1" ]

817782

2 3 7 19471

[ "817782 2 408891", "408891 3 136297", "136297 7 19471", "19471 19471 1" ]

1914898

2 37 113 229

[ "1914898 2 957449", "957449 37 25877", "25877 113 229", "229 229 1" ]

4620833

7 660119

[ "4620833 7 660119", "660119 660119 1" ]

2143341

3 3 3 3 47 563

[ "2143341 3 714447", "714447 3 238149", "238149 3 79383", "79383 3 26461", "26461 47 563", "563 563 1" ]

2480314

2 71 17467

[ "2480314 2 1240157", "1240157 71 17467", "17467 17467 1" ]

557966

2 227 1229

[ "557966 2 278983", "278983 227 1229", "1229 1229 1" ]

1793157

3 29 20611

[ "1793157 3 597719", "597719 29 20611", "20611 20611 1" ]

464816

2 2 2 2 11 19 139

[ "464816 2 232408", "232408 2 116204", "116204 2 58102", "58102 2 29051", "29051 11 2641", "2641 19 139", "139 139 1" ]

4992638

2 7 227 1571

[ "4992638 2 2496319", "2496319 7 356617", "356617 227 1571", "1571 1571 1" ]

334921

29 11549

[ "334921 29 11549", "11549 11549 1" ]

951802

2 67 7103

[ "951802 2 475901", "475901 67 7103", "7103 7103 1" ]

786857

29 43 631

[ "786857 29 27133", "27133 43 631", "631 631 1" ]

518201

29 107 167

[ "518201 29 17869", "17869 107 167", "167 167 1" ]

839941

571 1471

[ "839941 571 1471", "1471 1471 1" ]

4469963

17 17 15467

[ "4469963 17 262939", "262939 17 15467", "15467 15467 1" ]

4787303

617 7759

[ "4787303 617 7759", "7759 7759 1" ]

3623129

19 41 4651

[ "3623129 19 190691", "190691 41 4651", "4651 4651 1" ]

3696920

2 2 2 5 29 3187

[ "3696920 2 1848460", "1848460 2 924230", "924230 2 462115", "462115 5 92423", "92423 29 3187", "3187 3187 1" ]

3624038

2 11 164729

[ "3624038 2 1812019", "1812019 11 164729", "164729 164729 1" ]

4206977

547 7691

[ "4206977 547 7691", "7691 7691 1" ]

4719975

3 5 5 13 47 103

[ "4719975 3 1573325", "1573325 5 314665", "314665 5 62933", "62933 13 4841", "4841 47 103", "103 103 1" ]

1513733

13 13 13 13 53

[ "1513733 13 116441", "116441 13 8957", "8957 13 689", "689 13 53", "53 53 1" ]

2524079

59 179 239

[ "2524079 59 42781", "42781 179 239", "239 239 1" ]

3833120

2 2 2 2 2 5 23957

[ "3833120 2 1916560", "1916560 2 958280", "958280 2 479140", "479140 2 239570", "239570 2 119785", "119785 5 23957", "23957 23957 1" ]

1085948

2 2 73 3719

[ "1085948 2 542974", "542974 2 271487", "271487 73 3719", "3719 3719 1" ]

421055

5 84211

[ "421055 5 84211", "84211 84211 1" ]

4117181

[ "4117181 4117181 1" ]

460307

41 103 109

[ "460307 41 11227", "11227 103 109", "109 109 1" ]

617492

2 2 154373

[ "617492 2 308746", "308746 2 154373", "154373 154373 1" ]

500203

11 37 1229

[ "500203 11 45473", "45473 37 1229", "1229 1229 1" ]

3598600

2 2 2 5 5 19 947

[ "3598600 2 1799300", "1799300 2 899650", "899650 2 449825", "449825 5 89965", "89965 5 17993", "17993 19 947", "947 947 1" ]

4698576

2 2 2 2 3 3 67 487

[ "4698576 2 2349288", "2349288 2 1174644", "1174644 2 587322", "587322 2 293661", "293661 3 97887", "97887 3 32629", "32629 67 487", "487 487 1" ]

3565567

[ "3565567 3565567 1" ]

4425792

2 2 2 2 2 2 3 7 37 89

[ "4425792 2 2212896", "2212896 2 1106448", "1106448 2 553224", "553224 2 276612", "276612 2 138306", "138306 2 69153", "69153 3 23051", "23051 7 3293", "3293 37 89", "89 89 1" ]

1043945

5 7 7 4261

[ "1043945 5 208789", "208789 7 29827", "29827 7 4261", "4261 4261 1" ]

3782047

227 16661

[ "3782047 227 16661", "16661 16661 1" ]

152574

2 3 59 431

[ "152574 2 76287", "76287 3 25429", "25429 59 431", "431 431 1" ]

3174048

2 2 2 2 2 3 3 103 107

[ "3174048 2 1587024", "1587024 2 793512", "793512 2 396756", "396756 2 198378", "198378 2 99189", "99189 3 33063", "33063 3 11021", "11021 103 107", "107 107 1" ]

1818926

2 909463

[ "1818926 2 909463", "909463 909463 1" ]

2836346

2 37 38329

[ "2836346 2 1418173", "1418173 37 38329", "38329 38329 1" ]