yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
4603019	1289 3571	[ "4603019 1289 3571", "3571 3571 1" ]
2067227	37 55871	[ "2067227 37 55871", "55871 55871 1" ]
2544503	13 195731	[ "2544503 13 195731", "195731 195731 1" ]
136676	2 2 47 727	[ "136676 2 68338", "68338 2 34169", "34169 47 727", "727 727 1" ]
2327401	2327401	[ "2327401 2327401 1" ]
37734	2 3 19 331	[ "37734 2 18867", "18867 3 6289", "6289 19 331", "331 331 1" ]
3438257	1327 2591	[ "3438257 1327 2591", "2591 2591 1" ]
2237502	2 3 372917	[ "2237502 2 1118751", "1118751 3 372917", "372917 372917 1" ]
3845493	3 3 47 9091	[ "3845493 3 1281831", "1281831 3 427277", "427277 47 9091", "9091 9091 1" ]
2513294	2 7 31 5791	[ "2513294 2 1256647", "1256647 7 179521", "179521 31 5791", "5791 5791 1" ]
2237874	2 3 372979	[ "2237874 2 1118937", "1118937 3 372979", "372979 372979 1" ]
531769	7 75967	[ "531769 7 75967", "75967 75967 1" ]
980129	53 18493	[ "980129 53 18493", "18493 18493 1" ]
32135	5 6427	[ "32135 5 6427", "6427 6427 1" ]
3335713	23 145031	[ "3335713 23 145031", "145031 145031 1" ]
3530324	2 2 7 59 2137	[ "3530324 2 1765162", "1765162 2 882581", "882581 7 126083", "126083 59 2137", "2137 2137 1" ]
4245599	4245599	[ "4245599 4245599 1" ]
288397	23 12539	[ "288397 23 12539", "12539 12539 1" ]
2642034	2 3 440339	[ "2642034 2 1321017", "1321017 3 440339", "440339 440339 1" ]
3290537	17 41 4721	[ "3290537 17 193561", "193561 41 4721", "4721 4721 1" ]
2028889	73 27793	[ "2028889 73 27793", "27793 27793 1" ]
4905324	2 2 3 3 89 1531	[ "4905324 2 2452662", "2452662 2 1226331", "1226331 3 408777", "408777 3 136259", "136259 89 1531", "1531 1531 1" ]
422452	2 2 105613	[ "422452 2 211226", "211226 2 105613", "105613 105613 1" ]
2269644	2 2 3 13 14549	[ "2269644 2 1134822", "1134822 2 567411", "567411 3 189137", "189137 13 14549", "14549 14549 1" ]
4823851	4823851	[ "4823851 4823851 1" ]
4459517	109 163 251	[ "4459517 109 40913", "40913 163 251", "251 251 1" ]
3844941	3 17 75391	[ "3844941 3 1281647", "1281647 17 75391", "75391 75391 1" ]
1081359	3 3 53 2267	[ "1081359 3 360453", "360453 3 120151", "120151 53 2267", "2267 2267 1" ]
2879822	2 11 223 587	[ "2879822 2 1439911", "1439911 11 130901", "130901 223 587", "587 587 1" ]
2602394	2 17 76541	[ "2602394 2 1301197", "1301197 17 76541", "76541 76541 1" ]
3098129	61 50789	[ "3098129 61 50789", "50789 50789 1" ]
2365873	17 139169	[ "2365873 17 139169", "139169 139169 1" ]
1196065	5 13 18401	[ "1196065 5 239213", "239213 13 18401", "18401 18401 1" ]
2954178	2 3 3 3 227 241	[ "2954178 2 1477089", "1477089 3 492363", "492363 3 164121", "164121 3 54707", "54707 227 241", "241 241 1" ]
3191777	3191777	[ "3191777 3191777 1" ]
15729	3 7 7 107	[ "15729 3 5243", "5243 7 749", "749 7 107", "107 107 1" ]
2512005	3 5 17 9851	[ "2512005 3 837335", "837335 5 167467", "167467 17 9851", "9851 9851 1" ]
2328677	13 17 41 257	[ "2328677 13 179129", "179129 17 10537", "10537 41 257", "257 257 1" ]
3832914	2 3 638819	[ "3832914 2 1916457", "1916457 3 638819", "638819 638819 1" ]
4267911	3 1422637	[ "4267911 3 1422637", "1422637 1422637 1" ]
1198618	2 599309	[ "1198618 2 599309", "599309 599309 1" ]
1636377	3 199 2741	[ "1636377 3 545459", "545459 199 2741", "2741 2741 1" ]
710271	3 3 78919	[ "710271 3 236757", "236757 3 78919", "78919 78919 1" ]
887825	5 5 17 2089	[ "887825 5 177565", "177565 5 35513", "35513 17 2089", "2089 2089 1" ]
3858385	5 113 6829	[ "3858385 5 771677", "771677 113 6829", "6829 6829 1" ]
3760275	3 5 5 181 277	[ "3760275 3 1253425", "1253425 5 250685", "250685 5 50137", "50137 181 277", "277 277 1" ]
3848467	7 137 4013	[ "3848467 7 549781", "549781 137 4013", "4013 4013 1" ]
569236	2 2 101 1409	[ "569236 2 284618", "284618 2 142309", "142309 101 1409", "1409 1409 1" ]
527323	17 31019	[ "527323 17 31019", "31019 31019 1" ]
1574537	73 21569	[ "1574537 73 21569", "21569 21569 1" ]
3951021	3 17 77471	[ "3951021 3 1317007", "1317007 17 77471", "77471 77471 1" ]
2612388	2 2 3 293 743	[ "2612388 2 1306194", "1306194 2 653097", "653097 3 217699", "217699 293 743", "743 743 1" ]
4126517	271 15227	[ "4126517 271 15227", "15227 15227 1" ]
4193342	2 29 197 367	[ "4193342 2 2096671", "2096671 29 72299", "72299 197 367", "367 367 1" ]
1913550	2 3 5 5 12757	[ "1913550 2 956775", "956775 3 318925", "318925 5 63785", "63785 5 12757", "12757 12757 1" ]
4878974	2 2439487	[ "4878974 2 2439487", "2439487 2439487 1" ]
4299246	2 3 3 7 149 229	[ "4299246 2 2149623", "2149623 3 716541", "716541 3 238847", "238847 7 34121", "34121 149 229", "229 229 1" ]
4700690	2 5 277 1697	[ "4700690 2 2350345", "2350345 5 470069", "470069 277 1697", "1697 1697 1" ]
1936490	2 5 193649	[ "1936490 2 968245", "968245 5 193649", "193649 193649 1" ]
4026176	2 2 2 2 2 2 7 11 19 43	[ "4026176 2 2013088", "2013088 2 1006544", "1006544 2 503272", "503272 2 251636", "251636 2 125818", "125818 2 62909", "62909 7 8987", "8987 11 817", "817 19 43", "43 43 1" ]
1104557	1104557	[ "1104557 1104557 1" ]
4076808	2 2 2 3 37 4591	[ "4076808 2 2038404", "2038404 2 1019202", "1019202 2 509601", "509601 3 169867", "169867 37 4591", "4591 4591 1" ]
678959	678959	[ "678959 678959 1" ]
3540049	37 241 397	[ "3540049 37 95677", "95677 241 397", "397 397 1" ]
1906372	2 2 13 61 601	[ "1906372 2 953186", "953186 2 476593", "476593 13 36661", "36661 61 601", "601 601 1" ]
1540508	2 2 385127	[ "1540508 2 770254", "770254 2 385127", "385127 385127 1" ]
1369778	2 684889	[ "1369778 2 684889", "684889 684889 1" ]
3013300	2 2 5 5 30133	[ "3013300 2 1506650", "1506650 2 753325", "753325 5 150665", "150665 5 30133", "30133 30133 1" ]
3127720	2 2 2 5 78193	[ "3127720 2 1563860", "1563860 2 781930", "781930 2 390965", "390965 5 78193", "78193 78193 1" ]
3815915	5 763183	[ "3815915 5 763183", "763183 763183 1" ]
1916854	2 31 43 719	[ "1916854 2 958427", "958427 31 30917", "30917 43 719", "719 719 1" ]
4331045	5 197 4397	[ "4331045 5 866209", "866209 197 4397", "4397 4397 1" ]
1343223	3 3 3 3 7 23 103	[ "1343223 3 447741", "447741 3 149247", "149247 3 49749", "49749 3 16583", "16583 7 2369", "2369 23 103", "103 103 1" ]
3409516	2 2 11 77489	[ "3409516 2 1704758", "1704758 2 852379", "852379 11 77489", "77489 77489 1" ]
1860496	2 2 2 2 11 11 31 31	[ "1860496 2 930248", "930248 2 465124", "465124 2 232562", "232562 2 116281", "116281 11 10571", "10571 11 961", "961 31 31", "31 31 1" ]
1737742	2 23 37 1021	[ "1737742 2 868871", "868871 23 37777", "37777 37 1021", "1021 1021 1" ]
546535	5 11 19 523	[ "546535 5 109307", "109307 11 9937", "9937 19 523", "523 523 1" ]
2356134	2 3 11 29 1231	[ "2356134 2 1178067", "1178067 3 392689", "392689 11 35699", "35699 29 1231", "1231 1231 1" ]
3719406	2 3 71 8731	[ "3719406 2 1859703", "1859703 3 619901", "619901 71 8731", "8731 8731 1" ]
1784644	2 2 503 887	[ "1784644 2 892322", "892322 2 446161", "446161 503 887", "887 887 1" ]
1465437	3 661 739	[ "1465437 3 488479", "488479 661 739", "739 739 1" ]
1781400	2 2 2 3 5 5 2969	[ "1781400 2 890700", "890700 2 445350", "445350 2 222675", "222675 3 74225", "74225 5 14845", "14845 5 2969", "2969 2969 1" ]
1262617	1262617	[ "1262617 1262617 1" ]
1470374	2 735187	[ "1470374 2 735187", "735187 735187 1" ]
4882180	2 2 5 244109	[ "4882180 2 2441090", "2441090 2 1220545", "1220545 5 244109", "244109 244109 1" ]
4376799	3 3 7 69473	[ "4376799 3 1458933", "1458933 3 486311", "486311 7 69473", "69473 69473 1" ]
1389382	2 701 991	[ "1389382 2 694691", "694691 701 991", "991 991 1" ]
3836469	3 7 13 13 23 47	[ "3836469 3 1278823", "1278823 7 182689", "182689 13 14053", "14053 13 1081", "1081 23 47", "47 47 1" ]
2464837	2464837	[ "2464837 2464837 1" ]
1427192	2 2 2 13 13723	[ "1427192 2 713596", "713596 2 356798", "356798 2 178399", "178399 13 13723", "13723 13723 1" ]
590705	5 31 37 103	[ "590705 5 118141", "118141 31 3811", "3811 37 103", "103 103 1" ]
3771659	43 239 367	[ "3771659 43 87713", "87713 239 367", "367 367 1" ]
1868815	5 13 28751	[ "1868815 5 373763", "373763 13 28751", "28751 28751 1" ]
2865198	2 3 7 68219	[ "2865198 2 1432599", "1432599 3 477533", "477533 7 68219", "68219 68219 1" ]
1207791	3 3 3 3 13 31 37	[ "1207791 3 402597", "402597 3 134199", "134199 3 44733", "44733 3 14911", "14911 13 1147", "1147 31 37", "37 37 1" ]
2080572	2 2 3 13 13337	[ "2080572 2 1040286", "1040286 2 520143", "520143 3 173381", "173381 13 13337", "13337 13337 1" ]
1293078	2 3 61 3533	[ "1293078 2 646539", "646539 3 215513", "215513 61 3533", "3533 3533 1" ]
836289	3 3 92921	[ "836289 3 278763", "278763 3 92921", "92921 92921 1" ]
2797542	2 3 3 11 71 199	[ "2797542 2 1398771", "1398771 3 466257", "466257 3 155419", "155419 11 14129", "14129 71 199", "199 199 1" ]
4884813	3 3 3 227 797	[ "4884813 3 1628271", "1628271 3 542757", "542757 3 180919", "180919 227 797", "797 797 1" ]

4603019

1289 3571

[ "4603019 1289 3571", "3571 3571 1" ]

2067227

37 55871

[ "2067227 37 55871", "55871 55871 1" ]

2544503

13 195731

[ "2544503 13 195731", "195731 195731 1" ]

136676

2 2 47 727

[ "136676 2 68338", "68338 2 34169", "34169 47 727", "727 727 1" ]

2327401

[ "2327401 2327401 1" ]

37734

2 3 19 331

[ "37734 2 18867", "18867 3 6289", "6289 19 331", "331 331 1" ]

3438257

1327 2591

[ "3438257 1327 2591", "2591 2591 1" ]

2237502

2 3 372917

[ "2237502 2 1118751", "1118751 3 372917", "372917 372917 1" ]

3845493

3 3 47 9091

[ "3845493 3 1281831", "1281831 3 427277", "427277 47 9091", "9091 9091 1" ]

2513294

2 7 31 5791

[ "2513294 2 1256647", "1256647 7 179521", "179521 31 5791", "5791 5791 1" ]

2237874

2 3 372979

[ "2237874 2 1118937", "1118937 3 372979", "372979 372979 1" ]

531769

7 75967

[ "531769 7 75967", "75967 75967 1" ]

980129

53 18493

[ "980129 53 18493", "18493 18493 1" ]

32135

5 6427

[ "32135 5 6427", "6427 6427 1" ]

3335713

23 145031

[ "3335713 23 145031", "145031 145031 1" ]

3530324

2 2 7 59 2137

[ "3530324 2 1765162", "1765162 2 882581", "882581 7 126083", "126083 59 2137", "2137 2137 1" ]

4245599

[ "4245599 4245599 1" ]

288397

23 12539

[ "288397 23 12539", "12539 12539 1" ]

2642034

2 3 440339

[ "2642034 2 1321017", "1321017 3 440339", "440339 440339 1" ]

3290537

17 41 4721

[ "3290537 17 193561", "193561 41 4721", "4721 4721 1" ]

2028889

73 27793

[ "2028889 73 27793", "27793 27793 1" ]

4905324

2 2 3 3 89 1531

[ "4905324 2 2452662", "2452662 2 1226331", "1226331 3 408777", "408777 3 136259", "136259 89 1531", "1531 1531 1" ]

422452

2 2 105613

[ "422452 2 211226", "211226 2 105613", "105613 105613 1" ]

2269644

2 2 3 13 14549

[ "2269644 2 1134822", "1134822 2 567411", "567411 3 189137", "189137 13 14549", "14549 14549 1" ]

4823851

[ "4823851 4823851 1" ]

4459517

109 163 251

[ "4459517 109 40913", "40913 163 251", "251 251 1" ]

3844941

3 17 75391

[ "3844941 3 1281647", "1281647 17 75391", "75391 75391 1" ]

1081359

3 3 53 2267

[ "1081359 3 360453", "360453 3 120151", "120151 53 2267", "2267 2267 1" ]

2879822

2 11 223 587

[ "2879822 2 1439911", "1439911 11 130901", "130901 223 587", "587 587 1" ]

2602394

2 17 76541

[ "2602394 2 1301197", "1301197 17 76541", "76541 76541 1" ]

3098129

61 50789

[ "3098129 61 50789", "50789 50789 1" ]

2365873

17 139169

[ "2365873 17 139169", "139169 139169 1" ]

1196065

5 13 18401

[ "1196065 5 239213", "239213 13 18401", "18401 18401 1" ]

2954178

2 3 3 3 227 241

[ "2954178 2 1477089", "1477089 3 492363", "492363 3 164121", "164121 3 54707", "54707 227 241", "241 241 1" ]

3191777

[ "3191777 3191777 1" ]

15729

3 7 7 107

[ "15729 3 5243", "5243 7 749", "749 7 107", "107 107 1" ]

2512005

3 5 17 9851

[ "2512005 3 837335", "837335 5 167467", "167467 17 9851", "9851 9851 1" ]

2328677

13 17 41 257

[ "2328677 13 179129", "179129 17 10537", "10537 41 257", "257 257 1" ]

3832914

2 3 638819

[ "3832914 2 1916457", "1916457 3 638819", "638819 638819 1" ]

4267911

3 1422637

[ "4267911 3 1422637", "1422637 1422637 1" ]

1198618

2 599309

[ "1198618 2 599309", "599309 599309 1" ]

1636377

3 199 2741

[ "1636377 3 545459", "545459 199 2741", "2741 2741 1" ]

710271

3 3 78919

[ "710271 3 236757", "236757 3 78919", "78919 78919 1" ]

887825

5 5 17 2089

[ "887825 5 177565", "177565 5 35513", "35513 17 2089", "2089 2089 1" ]

3858385

5 113 6829

[ "3858385 5 771677", "771677 113 6829", "6829 6829 1" ]

3760275

3 5 5 181 277

[ "3760275 3 1253425", "1253425 5 250685", "250685 5 50137", "50137 181 277", "277 277 1" ]

3848467

7 137 4013

[ "3848467 7 549781", "549781 137 4013", "4013 4013 1" ]

569236

2 2 101 1409

[ "569236 2 284618", "284618 2 142309", "142309 101 1409", "1409 1409 1" ]

527323

17 31019

[ "527323 17 31019", "31019 31019 1" ]

1574537

73 21569

[ "1574537 73 21569", "21569 21569 1" ]

3951021

3 17 77471

[ "3951021 3 1317007", "1317007 17 77471", "77471 77471 1" ]

2612388

2 2 3 293 743

[ "2612388 2 1306194", "1306194 2 653097", "653097 3 217699", "217699 293 743", "743 743 1" ]

4126517

271 15227

[ "4126517 271 15227", "15227 15227 1" ]

4193342

2 29 197 367

[ "4193342 2 2096671", "2096671 29 72299", "72299 197 367", "367 367 1" ]

1913550

2 3 5 5 12757

[ "1913550 2 956775", "956775 3 318925", "318925 5 63785", "63785 5 12757", "12757 12757 1" ]

4878974

2 2439487

[ "4878974 2 2439487", "2439487 2439487 1" ]

4299246

2 3 3 7 149 229

[ "4299246 2 2149623", "2149623 3 716541", "716541 3 238847", "238847 7 34121", "34121 149 229", "229 229 1" ]

4700690

2 5 277 1697

[ "4700690 2 2350345", "2350345 5 470069", "470069 277 1697", "1697 1697 1" ]

1936490

2 5 193649

[ "1936490 2 968245", "968245 5 193649", "193649 193649 1" ]

4026176

2 2 2 2 2 2 7 11 19 43

[ "4026176 2 2013088", "2013088 2 1006544", "1006544 2 503272", "503272 2 251636", "251636 2 125818", "125818 2 62909", "62909 7 8987", "8987 11 817", "817 19 43", "43 43 1" ]

1104557

[ "1104557 1104557 1" ]

4076808

2 2 2 3 37 4591

[ "4076808 2 2038404", "2038404 2 1019202", "1019202 2 509601", "509601 3 169867", "169867 37 4591", "4591 4591 1" ]

678959

[ "678959 678959 1" ]

3540049

37 241 397

[ "3540049 37 95677", "95677 241 397", "397 397 1" ]

1906372

2 2 13 61 601

[ "1906372 2 953186", "953186 2 476593", "476593 13 36661", "36661 61 601", "601 601 1" ]

1540508

2 2 385127

[ "1540508 2 770254", "770254 2 385127", "385127 385127 1" ]

1369778

2 684889

[ "1369778 2 684889", "684889 684889 1" ]

3013300

2 2 5 5 30133

[ "3013300 2 1506650", "1506650 2 753325", "753325 5 150665", "150665 5 30133", "30133 30133 1" ]

3127720

2 2 2 5 78193

[ "3127720 2 1563860", "1563860 2 781930", "781930 2 390965", "390965 5 78193", "78193 78193 1" ]

3815915

5 763183

[ "3815915 5 763183", "763183 763183 1" ]

1916854

2 31 43 719

[ "1916854 2 958427", "958427 31 30917", "30917 43 719", "719 719 1" ]

4331045

5 197 4397

[ "4331045 5 866209", "866209 197 4397", "4397 4397 1" ]

1343223

3 3 3 3 7 23 103

[ "1343223 3 447741", "447741 3 149247", "149247 3 49749", "49749 3 16583", "16583 7 2369", "2369 23 103", "103 103 1" ]

3409516

2 2 11 77489

[ "3409516 2 1704758", "1704758 2 852379", "852379 11 77489", "77489 77489 1" ]

1860496

2 2 2 2 11 11 31 31

[ "1860496 2 930248", "930248 2 465124", "465124 2 232562", "232562 2 116281", "116281 11 10571", "10571 11 961", "961 31 31", "31 31 1" ]

1737742

2 23 37 1021

[ "1737742 2 868871", "868871 23 37777", "37777 37 1021", "1021 1021 1" ]

546535

5 11 19 523

[ "546535 5 109307", "109307 11 9937", "9937 19 523", "523 523 1" ]

2356134

2 3 11 29 1231

[ "2356134 2 1178067", "1178067 3 392689", "392689 11 35699", "35699 29 1231", "1231 1231 1" ]

3719406

2 3 71 8731

[ "3719406 2 1859703", "1859703 3 619901", "619901 71 8731", "8731 8731 1" ]

1784644

2 2 503 887

[ "1784644 2 892322", "892322 2 446161", "446161 503 887", "887 887 1" ]

1465437

3 661 739

[ "1465437 3 488479", "488479 661 739", "739 739 1" ]

1781400

2 2 2 3 5 5 2969

[ "1781400 2 890700", "890700 2 445350", "445350 2 222675", "222675 3 74225", "74225 5 14845", "14845 5 2969", "2969 2969 1" ]

1262617

[ "1262617 1262617 1" ]

1470374

2 735187

[ "1470374 2 735187", "735187 735187 1" ]

4882180

2 2 5 244109

[ "4882180 2 2441090", "2441090 2 1220545", "1220545 5 244109", "244109 244109 1" ]

4376799

3 3 7 69473

[ "4376799 3 1458933", "1458933 3 486311", "486311 7 69473", "69473 69473 1" ]

1389382

2 701 991

[ "1389382 2 694691", "694691 701 991", "991 991 1" ]

3836469

3 7 13 13 23 47

[ "3836469 3 1278823", "1278823 7 182689", "182689 13 14053", "14053 13 1081", "1081 23 47", "47 47 1" ]

2464837

[ "2464837 2464837 1" ]

1427192

2 2 2 13 13723

[ "1427192 2 713596", "713596 2 356798", "356798 2 178399", "178399 13 13723", "13723 13723 1" ]

590705

5 31 37 103

[ "590705 5 118141", "118141 31 3811", "3811 37 103", "103 103 1" ]

3771659

43 239 367

[ "3771659 43 87713", "87713 239 367", "367 367 1" ]

1868815

5 13 28751

[ "1868815 5 373763", "373763 13 28751", "28751 28751 1" ]

2865198

2 3 7 68219

[ "2865198 2 1432599", "1432599 3 477533", "477533 7 68219", "68219 68219 1" ]

1207791

3 3 3 3 13 31 37

[ "1207791 3 402597", "402597 3 134199", "134199 3 44733", "44733 3 14911", "14911 13 1147", "1147 31 37", "37 37 1" ]

2080572

2 2 3 13 13337

[ "2080572 2 1040286", "1040286 2 520143", "520143 3 173381", "173381 13 13337", "13337 13337 1" ]

1293078

2 3 61 3533

[ "1293078 2 646539", "646539 3 215513", "215513 61 3533", "3533 3533 1" ]

836289

3 3 92921

[ "836289 3 278763", "278763 3 92921", "92921 92921 1" ]

2797542

2 3 3 11 71 199

[ "2797542 2 1398771", "1398771 3 466257", "466257 3 155419", "155419 11 14129", "14129 71 199", "199 199 1" ]

4884813

3 3 3 227 797

[ "4884813 3 1628271", "1628271 3 542757", "542757 3 180919", "180919 227 797", "797 797 1" ]