Below is a list of the first 1000 semiprimes, the product of two prime numbers, both approximately the same size. The criterion we chose is that the larger factor must be less than twice the smaller factor. In other words, both factors must have approximately the same number of bits. This criterion, for much larger semiprimes, is good for RSA cryptography.
Tangentially, other less restrictive criteria we could have chosen but didn't:
- No restrictions on the relative sizes of the two prime factors. Such a list would still exclude composites which have 3 or more prime factors.
- The larger factor must be less than the square of the smaller factor. In other words, no more than twice the number of digits
Perfect squares are permitted on our list below. (But they should not be permitted as RSA moduli.)
Previously, on rectangles that are squarish.
It might be fun to try to memorize the first few semiprimes and their factorizations, say, up to 1000 (the first 36). The brain unconsciously organizes things.
What is the growth rate of the sequence? This is probably not difficult to derive from the Prime Number Theorem.
Here is some Haskell code to compute the list in order.. We use Data.List.Ordered.mergeAll from the ordered-list package. Previously, on this handy package.
4 = 2 * 2
6 = 2 * 3
9 = 3 * 3
15 = 3 * 5
25 = 5 * 5
35 = 5 * 7
49 = 7 * 7
77 = 7 * 11
91 = 7 * 13
121 = 11 * 11
143 = 11 * 13
169 = 13 * 13
187 = 11 * 17
209 = 11 * 19
221 = 13 * 17
247 = 13 * 19
289 = 17 * 17
299 = 13 * 23
323 = 17 * 19
361 = 19 * 19
391 = 17 * 23
437 = 19 * 23
493 = 17 * 29
527 = 17 * 31
529 = 23 * 23
551 = 19 * 29
589 = 19 * 31
667 = 23 * 29
703 = 19 * 37
713 = 23 * 31
841 = 29 * 29
851 = 23 * 37
899 = 29 * 31
943 = 23 * 41
961 = 31 * 31
989 = 23 * 43
1073 = 29 * 37
1147 = 31 * 37
1189 = 29 * 41
1247 = 29 * 43
1271 = 31 * 41
1333 = 31 * 43
1363 = 29 * 47
1369 = 37 * 37
1457 = 31 * 47
1517 = 37 * 41
1537 = 29 * 53
1591 = 37 * 43
1643 = 31 * 53
1681 = 41 * 41
1739 = 37 * 47
1763 = 41 * 43
1829 = 31 * 59
1849 = 43 * 43
1891 = 31 * 61
1927 = 41 * 47
1961 = 37 * 53
2021 = 43 * 47
2173 = 41 * 53
2183 = 37 * 59
2209 = 47 * 47
2257 = 37 * 61
2279 = 43 * 53
2419 = 41 * 59
2479 = 37 * 67
2491 = 47 * 53
2501 = 41 * 61
2537 = 43 * 59
2623 = 43 * 61
2627 = 37 * 71
2701 = 37 * 73
2747 = 41 * 67
2773 = 47 * 59
2809 = 53 * 53
2867 = 47 * 61
2881 = 43 * 67
2911 = 41 * 71
2993 = 41 * 73
3053 = 43 * 71
3127 = 53 * 59
3139 = 43 * 73
3149 = 47 * 67
3233 = 53 * 61
3239 = 41 * 79
3337 = 47 * 71
3397 = 43 * 79
3431 = 47 * 73
3481 = 59 * 59
3551 = 53 * 67
3569 = 43 * 83
3599 = 59 * 61
3713 = 47 * 79
3721 = 61 * 61
3763 = 53 * 71
3869 = 53 * 73
3901 = 47 * 83
3953 = 59 * 67
4087 = 61 * 67
4183 = 47 * 89
4187 = 53 * 79
4189 = 59 * 71
4307 = 59 * 73
4331 = 61 * 71
4399 = 53 * 83
4453 = 61 * 73
4489 = 67 * 67
4661 = 59 * 79
4717 = 53 * 89
4757 = 67 * 71
4819 = 61 * 79
4891 = 67 * 73
4897 = 59 * 83
5041 = 71 * 71
5063 = 61 * 83
5141 = 53 * 97
5183 = 71 * 73
5251 = 59 * 89
5293 = 67 * 79
5329 = 73 * 73
5353 = 53 * 101
5429 = 61 * 89
5459 = 53 * 103
5561 = 67 * 83
5609 = 71 * 79
5723 = 59 * 97
5767 = 73 * 79
5893 = 71 * 83
5917 = 61 * 97
5959 = 59 * 101
5963 = 67 * 89
6059 = 73 * 83
6077 = 59 * 103
6161 = 61 * 101
6241 = 79 * 79
6283 = 61 * 103
6313 = 59 * 107
6319 = 71 * 89
6431 = 59 * 109
6497 = 73 * 89
6499 = 67 * 97
6527 = 61 * 107
6557 = 79 * 83
6649 = 61 * 109
6667 = 59 * 113
6767 = 67 * 101
6887 = 71 * 97
6889 = 83 * 83
6893 = 61 * 113
6901 = 67 * 103
7031 = 79 * 89
7081 = 73 * 97
7169 = 67 * 107
7171 = 71 * 101
7303 = 67 * 109
7313 = 71 * 103
7373 = 73 * 101
7387 = 83 * 89
7519 = 73 * 103
7571 = 67 * 113
7597 = 71 * 107
7663 = 79 * 97
7739 = 71 * 109
7811 = 73 * 107
7921 = 89 * 89
7957 = 73 * 109
7979 = 79 * 101
8023 = 71 * 113
8051 = 83 * 97
8137 = 79 * 103
8249 = 73 * 113
8383 = 83 * 101
8453 = 79 * 107
8509 = 67 * 127
8549 = 83 * 103
8611 = 79 * 109
8633 = 89 * 97
8777 = 67 * 131
8881 = 83 * 107
8927 = 79 * 113
8989 = 89 * 101
9017 = 71 * 127
9047 = 83 * 109
9167 = 89 * 103
9271 = 73 * 127
9301 = 71 * 131
9379 = 83 * 113
9409 = 97 * 97
9523 = 89 * 107
9563 = 73 * 131
9701 = 89 * 109
9727 = 71 * 137
9797 = 97 * 101
9869 = 71 * 139
9991 = 97 * 103
10001 = 73 * 137
10033 = 79 * 127
10057 = 89 * 113
10147 = 73 * 139
10201 = 101 * 101
10349 = 79 * 131
10379 = 97 * 107
10403 = 101 * 103
10541 = 83 * 127
10573 = 97 * 109
10609 = 103 * 103
10807 = 101 * 107
10823 = 79 * 137
10873 = 83 * 131
10961 = 97 * 113
10981 = 79 * 139
11009 = 101 * 109
11021 = 103 * 107
11227 = 103 * 109
11303 = 89 * 127
11371 = 83 * 137
11413 = 101 * 113
11449 = 107 * 107
11537 = 83 * 139
11639 = 103 * 113
11659 = 89 * 131
11663 = 107 * 109
11771 = 79 * 149
11881 = 109 * 109
11929 = 79 * 151
12091 = 107 * 113
12193 = 89 * 137
12317 = 109 * 113
12319 = 97 * 127
12367 = 83 * 149
12371 = 89 * 139
12403 = 79 * 157
12533 = 83 * 151
12707 = 97 * 131
12769 = 113 * 113
12827 = 101 * 127
13031 = 83 * 157
13081 = 103 * 127
13231 = 101 * 131
13261 = 89 * 149
13289 = 97 * 137
13439 = 89 * 151
13483 = 97 * 139
13493 = 103 * 131
13529 = 83 * 163
13589 = 107 * 127
13837 = 101 * 137
13843 = 109 * 127
13973 = 89 * 157
14017 = 107 * 131
14039 = 101 * 139
14111 = 103 * 137
14279 = 109 * 131
14317 = 103 * 139
14351 = 113 * 127
14453 = 97 * 149
14507 = 89 * 163
14647 = 97 * 151
14659 = 107 * 137
14803 = 113 * 131
14863 = 89 * 167
14873 = 107 * 139
14933 = 109 * 137
15049 = 101 * 149
15151 = 109 * 139
15229 = 97 * 157
15251 = 101 * 151
15347 = 103 * 149
15397 = 89 * 173
15481 = 113 * 137
15553 = 103 * 151
15707 = 113 * 139
15811 = 97 * 163
15857 = 101 * 157
15943 = 107 * 149
16129 = 127 * 127
16157 = 107 * 151
16171 = 103 * 157
16199 = 97 * 167
16241 = 109 * 149
16459 = 109 * 151
16463 = 101 * 163
16637 = 127 * 131
16781 = 97 * 173
16789 = 103 * 163
16799 = 107 * 157
16837 = 113 * 149
16867 = 101 * 167
17063 = 113 * 151
17113 = 109 * 157
17161 = 131 * 131
17201 = 103 * 167
17363 = 97 * 179
17399 = 127 * 137
17441 = 107 * 163
17473 = 101 * 173
17557 = 97 * 181
17653 = 127 * 139
17741 = 113 * 157
17767 = 109 * 163
17819 = 103 * 173
17869 = 107 * 167
17947 = 131 * 137
18079 = 101 * 179
18203 = 109 * 167
18209 = 131 * 139
18281 = 101 * 181
18419 = 113 * 163
18437 = 103 * 179
18511 = 107 * 173
18527 = 97 * 191
18643 = 103 * 181
18721 = 97 * 193
18769 = 137 * 137
18857 = 109 * 173
18871 = 113 * 167
18923 = 127 * 149
19043 = 137 * 139
19153 = 107 * 179
19177 = 127 * 151
19291 = 101 * 191
19321 = 139 * 139
19367 = 107 * 181
19493 = 101 * 193
19511 = 109 * 179
19519 = 131 * 149
19549 = 113 * 173
19673 = 103 * 191
19729 = 109 * 181
19781 = 131 * 151
19879 = 103 * 193
19897 = 101 * 197
19939 = 127 * 157
20099 = 101 * 199
20227 = 113 * 179
20291 = 103 * 197
20413 = 137 * 149
20437 = 107 * 191
20453 = 113 * 181
20497 = 103 * 199
20567 = 131 * 157
20651 = 107 * 193
20687 = 137 * 151
20701 = 127 * 163
20711 = 139 * 149
20819 = 109 * 191
20989 = 139 * 151
21037 = 109 * 193
21079 = 107 * 197
21209 = 127 * 167
21293 = 107 * 199
21353 = 131 * 163
21473 = 109 * 197
21509 = 137 * 157
21583 = 113 * 191
21691 = 109 * 199
21809 = 113 * 193
21823 = 139 * 157
21877 = 131 * 167
21971 = 127 * 173
22201 = 149 * 149
22261 = 113 * 197
22331 = 137 * 163
22487 = 113 * 199
22499 = 149 * 151
22577 = 107 * 211
22657 = 139 * 163
22663 = 131 * 173
22733 = 127 * 179
22801 = 151 * 151
22879 = 137 * 167
22987 = 127 * 181
22999 = 109 * 211
23213 = 139 * 167
23393 = 149 * 157
23449 = 131 * 179
23701 = 137 * 173
23707 = 151 * 157
23711 = 131 * 181
23843 = 113 * 211
24047 = 139 * 173
24257 = 127 * 191
24287 = 149 * 163
24511 = 127 * 193
24523 = 137 * 179
24613 = 151 * 163
24649 = 157 * 157
24797 = 137 * 181
24881 = 139 * 179
24883 = 149 * 167
25019 = 127 * 197
25021 = 131 * 191
25159 = 139 * 181
25199 = 113 * 223
25217 = 151 * 167
25273 = 127 * 199
25283 = 131 * 193
25591 = 157 * 163
25777 = 149 * 173
25807 = 131 * 197
26069 = 131 * 199
26123 = 151 * 173
26167 = 137 * 191
26219 = 157 * 167
26441 = 137 * 193
26549 = 139 * 191
26569 = 163 * 163
26671 = 149 * 179
26797 = 127 * 211
26827 = 139 * 193
26969 = 149 * 181
26989 = 137 * 197
27029 = 151 * 179
27161 = 157 * 173
27221 = 163 * 167
27263 = 137 * 199
27331 = 151 * 181
27383 = 139 * 197
27641 = 131 * 211
27661 = 139 * 199
27889 = 167 * 167
28103 = 157 * 179
28199 = 163 * 173
28321 = 127 * 223
28417 = 157 * 181
28459 = 149 * 191
28757 = 149 * 193
28829 = 127 * 227
28841 = 151 * 191
28891 = 167 * 173
28907 = 137 * 211
29083 = 127 * 229
29143 = 151 * 193
29177 = 163 * 179
29213 = 131 * 223
29329 = 139 * 211
29353 = 149 * 197
29503 = 163 * 181
29591 = 127 * 233
29651 = 149 * 199
29737 = 131 * 227
29747 = 151 * 197
29893 = 167 * 179
29929 = 173 * 173
29987 = 157 * 191
29999 = 131 * 229
30049 = 151 * 199
30227 = 167 * 181
30301 = 157 * 193
30353 = 127 * 239
30523 = 131 * 233
30551 = 137 * 223
30607 = 127 * 241
30929 = 157 * 197
30967 = 173 * 179
30997 = 139 * 223
31099 = 137 * 227
31133 = 163 * 191
31243 = 157 * 199
31309 = 131 * 239
31313 = 173 * 181
31373 = 137 * 229
31439 = 149 * 211
31459 = 163 * 193
31553 = 139 * 227
31571 = 131 * 241
31831 = 139 * 229
31861 = 151 * 211
31877 = 127 * 251
31897 = 167 * 191
31921 = 137 * 233
32041 = 179 * 179
32111 = 163 * 197
32231 = 167 * 193
32387 = 139 * 233
32399 = 179 * 181
32437 = 163 * 199
32743 = 137 * 239
32761 = 181 * 181
32881 = 131 * 251
32899 = 167 * 197
33017 = 137 * 241
33043 = 173 * 191
33127 = 157 * 211
33221 = 139 * 239
33227 = 149 * 223
33233 = 167 * 199
33389 = 173 * 193
33499 = 139 * 241
33667 = 131 * 257
33673 = 151 * 223
33823 = 149 * 227
34081 = 173 * 197
34121 = 149 * 229
34189 = 179 * 191
34277 = 151 * 227
34387 = 137 * 251
34393 = 163 * 211
34427 = 173 * 199
34547 = 179 * 193
34571 = 181 * 191
34579 = 151 * 229
34717 = 149 * 233
34889 = 139 * 251
34933 = 181 * 193
35011 = 157 * 223
35183 = 151 * 233
35209 = 137 * 257
35237 = 167 * 211
35263 = 179 * 197
35611 = 149 * 239
35621 = 179 * 199
35639 = 157 * 227
35657 = 181 * 197
35723 = 139 * 257
35909 = 149 * 241
35953 = 157 * 229
36019 = 181 * 199
36031 = 137 * 263
36089 = 151 * 239
36349 = 163 * 223
36391 = 151 * 241
36481 = 191 * 191
36503 = 173 * 211
36557 = 139 * 263
36581 = 157 * 233
36853 = 137 * 269
36863 = 191 * 193
37001 = 163 * 227
37127 = 137 * 271
37241 = 167 * 223
37249 = 193 * 193
37327 = 163 * 229
37391 = 139 * 269
37399 = 149 * 251
37523 = 157 * 239
37627 = 191 * 197
37669 = 139 * 271
37769 = 179 * 211
37837 = 157 * 241
37901 = 151 * 251
37909 = 167 * 227
37979 = 163 * 233
38009 = 191 * 199
38021 = 193 * 197
38191 = 181 * 211
38243 = 167 * 229
38293 = 149 * 257
38407 = 193 * 199
38503 = 139 * 277
38579 = 173 * 223
38807 = 151 * 257
38809 = 197 * 197
38911 = 167 * 233
38957 = 163 * 239
39187 = 149 * 263
39203 = 197 * 199
39271 = 173 * 227
39283 = 163 * 241
39407 = 157 * 251
39601 = 199 * 199
39617 = 173 * 229
39713 = 151 * 263
39913 = 167 * 239
39917 = 179 * 223
40081 = 149 * 269
40247 = 167 * 241
40301 = 191 * 211
40309 = 173 * 233
40349 = 157 * 257
40363 = 181 * 223
40379 = 149 * 271
40619 = 151 * 269
40633 = 179 * 227
40723 = 193 * 211
40913 = 163 * 251
40921 = 151 * 271
40991 = 179 * 229
41087 = 181 * 227
41273 = 149 * 277
41291 = 157 * 263
41347 = 173 * 239
41449 = 181 * 229
41567 = 197 * 211
41693 = 173 * 241
41707 = 179 * 233
41827 = 151 * 277
41869 = 149 * 281
41891 = 163 * 257
41917 = 167 * 251
41989 = 199 * 211
42167 = 149 * 283
42173 = 181 * 233
42233 = 157 * 269
42431 = 151 * 281
42547 = 157 * 271
42593 = 191 * 223
42733 = 151 * 283
42781 = 179 * 239
42869 = 163 * 263
42919 = 167 * 257
43039 = 193 * 223
43139 = 179 * 241
43259 = 181 * 239
43357 = 191 * 227
43423 = 173 * 251
43489 = 157 * 277
43621 = 181 * 241
43657 = 149 * 293
43739 = 191 * 229
43811 = 193 * 227
43847 = 163 * 269
43921 = 167 * 263
43931 = 197 * 223
44117 = 157 * 281
44173 = 163 * 271
44197 = 193 * 229
44243 = 151 * 293
44377 = 199 * 223
44431 = 157 * 283
44461 = 173 * 257
44503 = 191 * 233
44521 = 211 * 211
44719 = 197 * 227
44923 = 167 * 269
44929 = 179 * 251
44969 = 193 * 233
45113 = 197 * 229
45151 = 163 * 277
45173 = 199 * 227
45257 = 167 * 271
45431 = 181 * 251
45499 = 173 * 263
45571 = 199 * 229
45649 = 191 * 239
45803 = 163 * 281
45901 = 197 * 233
46001 = 157 * 293
46003 = 179 * 257
46031 = 191 * 241
46127 = 193 * 239
46129 = 163 * 283
46259 = 167 * 277
46367 = 199 * 233
46513 = 193 * 241
46517 = 181 * 257
46537 = 173 * 269
46883 = 173 * 271
46927 = 167 * 281
47053 = 211 * 223
47077 = 179 * 263
47083 = 197 * 239
47261 = 167 * 283
47477 = 197 * 241
47561 = 199 * 239
47603 = 181 * 263
47759 = 163 * 293
47897 = 211 * 227
47921 = 173 * 277
47941 = 191 * 251
47959 = 199 * 241
48151 = 179 * 269
48199 = 157 * 307
48319 = 211 * 229
48443 = 193 * 251
48509 = 179 * 271
48613 = 173 * 281
48689 = 181 * 269
48827 = 157 * 311
48931 = 167 * 293
48959 = 173 * 283
49051 = 181 * 271
49087 = 191 * 257
49141 = 157 * 313
49163 = 211 * 233
49447 = 197 * 251
49583 = 179 * 277
49601 = 193 * 257
49729 = 223 * 223
49949 = 199 * 251
50041 = 163 * 307
50137 = 181 * 277
50233 = 191 * 263
50299 = 179 * 281
50429 = 211 * 239
50621 = 223 * 227
50629 = 197 * 257
50657 = 179 * 283
50689 = 173 * 293
50693 = 163 * 311
50759 = 193 * 263
50851 = 211 * 241
50861 = 181 * 281
51019 = 163 * 313
51067 = 223 * 229
51143 = 199 * 257
51223 = 181 * 283
51269 = 167 * 307
51379 = 191 * 269
51529 = 227 * 227
51671 = 163 * 317
51761 = 191 * 271
51811 = 197 * 263
51917 = 193 * 269
51937 = 167 * 311
51959 = 223 * 233
51983 = 227 * 229
52271 = 167 * 313
52303 = 193 * 271
52337 = 199 * 263
52441 = 229 * 229
52447 = 179 * 293
52891 = 227 * 233
52907 = 191 * 277
52939 = 167 * 317
52961 = 211 * 251
52993 = 197 * 269
53033 = 181 * 293
53111 = 173 * 307
53297 = 223 * 239
53357 = 229 * 233
53387 = 197 * 271
53461 = 193 * 277
53531 = 199 * 269
53671 = 191 * 281
53743 = 223 * 241
53803 = 173 * 311
53929 = 199 * 271
54053 = 191 * 283
54149 = 173 * 313
54227 = 211 * 257
54233 = 193 * 281
54253 = 227 * 239
54289 = 233 * 233
54569 = 197 * 277
54619 = 193 * 283
54707 = 227 * 241
54731 = 229 * 239
54841 = 173 * 317
54953 = 179 * 307
55123 = 199 * 277
55189 = 229 * 241
55277 = 167 * 331
55357 = 197 * 281
55493 = 211 * 263
55567 = 181 * 307
55669 = 179 * 311
55687 = 233 * 239
55751 = 197 * 283
55919 = 199 * 281
55963 = 191 * 293
55973 = 223 * 251
56027 = 179 * 313
56153 = 233 * 241
56291 = 181 * 311
56317 = 199 * 283
56549 = 193 * 293
56653 = 181 * 313
56743 = 179 * 317
56759 = 211 * 269
56977 = 227 * 251
57121 = 239 * 239
57181 = 211 * 271
57263 = 173 * 331
57311 = 223 * 257
57377 = 181 * 317
57479 = 229 * 251
57599 = 239 * 241
57721 = 197 * 293
58081 = 241 * 241
58301 = 173 * 337
58307 = 199 * 293
58339 = 227 * 257
58447 = 211 * 277
58483 = 233 * 251
58637 = 191 * 307
58649 = 223 * 263
58853 = 229 * 257
59249 = 179 * 331
59251 = 193 * 307
59291 = 211 * 281
59401 = 191 * 311
59701 = 227 * 263
59713 = 211 * 283
59783 = 191 * 313
59881 = 233 * 257
59911 = 181 * 331
59987 = 223 * 269
59989 = 239 * 251
60023 = 193 * 311
60227 = 229 * 263
60323 = 179 * 337
60409 = 193 * 313
60433 = 223 * 271
60479 = 197 * 307
60491 = 241 * 251
60547 = 191 * 317
60997 = 181 * 337
61063 = 227 * 269
61093 = 199 * 307
61181 = 193 * 317
61267 = 197 * 311
61279 = 233 * 263
61423 = 239 * 257
61517 = 227 * 271
61601 = 229 * 269
61661 = 197 * 313
61771 = 223 * 277
61823 = 211 * 293
61889 = 199 * 311
61937 = 241 * 257
62059 = 229 * 271
62113 = 179 * 347
62287 = 199 * 313
62449 = 197 * 317
62471 = 179 * 349
62663 = 223 * 281
62677 = 233 * 269
62807 = 181 * 347
62857 = 239 * 263
62879 = 227 * 277
63001 = 251 * 251
63083 = 199 * 317
63109 = 223 * 283
63143 = 233 * 271
63169 = 181 * 349
63187 = 179 * 353
63221 = 191 * 331
63383 = 241 * 263
63433 = 229 * 277
63787 = 227 * 281
63883 = 193 * 331
63893 = 181 * 353
64241 = 227 * 283
64291 = 239 * 269
64349 = 229 * 281
64367 = 191 * 337
64507 = 251 * 257
64541 = 233 * 277
64769 = 239 * 271
64777 = 211 * 307
64807 = 229 * 283
64829 = 241 * 269
64979 = 181 * 359
65041 = 193 * 337
65207 = 197 * 331
65311 = 241 * 271
65339 = 223 * 293
65473 = 233 * 281
65621 = 211 * 311
65869 = 199 * 331
65939 = 233 * 283
66013 = 251 * 263
66043 = 211 * 313
66049 = 257 * 257
66203 = 239 * 277
66277 = 191 * 347
66389 = 197 * 337
66511 = 227 * 293
66659 = 191 * 349
66757 = 241 * 277
66887 = 211 * 317
66971 = 193 * 347
67063 = 199 * 337
67097 = 229 * 293
67159 = 239 * 281
67357 = 193 * 349
67423 = 191 * 353
67519 = 251 * 269
67591 = 257 * 263
67637 = 239 * 283
67721 = 241 * 281
68021 = 251 * 271
68129 = 193 * 353
68203 = 241 * 283
68269 = 233 * 293
68359 = 197 * 347
68461 = 223 * 307
68569 = 191 * 359
68753 = 197 * 349
69053 = 199 * 347
69133 = 257 * 269
69169 = 263 * 263
69287 = 193 * 359
69353 = 223 * 311
69451 = 199 * 349
69527 = 251 * 277
69541 = 197 * 353
69647 = 257 * 271
69689 = 227 * 307
69799 = 223 * 313
69841 = 211 * 331
70027 = 239 * 293
70097 = 191 * 367
70247 = 199 * 353
70303 = 229 * 307
70531 = 251 * 281
70597 = 227 * 311
70613 = 241 * 293
70691 = 223 * 317
70723 = 197 * 359
70747 = 263 * 269
70831 = 193 * 367
71033 = 251 * 283
71051 = 227 * 313
71107 = 211 * 337
71189 = 257 * 277
71219 = 229 * 311
71243 = 191 * 373
71273 = 263 * 271
71441 = 199 * 359
71531 = 233 * 307
71677 = 229 * 313
71959 = 227 * 317
71989 = 193 * 373
72217 = 257 * 281
72299 = 197 * 367
72361 = 269 * 269
72389 = 191 * 379
72463 = 233 * 311
72593 = 229 * 317
72731 = 257 * 283
72851 = 263 * 277
72899 = 269 * 271
72929 = 233 * 313
73033 = 199 * 367
73147 = 193 * 379
73217 = 211 * 347
73373 = 239 * 307
73441 = 271 * 271
73481 = 197 * 373
73543 = 251 * 293
73639 = 211 * 349
73813 = 223 * 331
73861 = 233 * 317
73903 = 263 * 281
73919 = 193 * 383
73987 = 241 * 307
74227 = 199 * 373
74329 = 239 * 311
74429 = 263 * 283
74483 = 211 * 353
74513 = 269 * 277
74663 = 197 * 379
74807 = 239 * 313
74951 = 241 * 311
75067 = 271 * 277
75137 = 227 * 331
75151 = 223 * 337
75301 = 257 * 293
75421 = 199 * 379
75433 = 241 * 313
75451 = 197 * 383
75589 = 269 * 281
75749 = 211 * 359
75763 = 239 * 317
75799 = 229 * 331
76127 = 269 * 283
76151 = 271 * 281
76217 = 199 * 383
76397 = 241 * 317
76499 = 227 * 337
76633 = 197 * 389
76693 = 271 * 283
76729 = 277 * 277
77057 = 251 * 307
77059 = 263 * 293
77123 = 233 * 331
77173 = 229 * 337
77381 = 223 * 347
77411 = 199 * 389
77437 = 211 * 367
77827 = 223 * 349
77837 = 277 * 281
78061 = 251 * 311
78391 = 277 * 283
78521 = 233 * 337
78563 = 251 * 313
78703 = 211 * 373
78719 = 223 * 353
78769 = 227 * 347
78817 = 269 * 293
78899 = 257 * 307
78961 = 281 * 281
79003 = 199 * 397
79109 = 239 * 331
79223 = 227 * 349
79403 = 271 * 293
79463 = 229 * 347
79523 = 281 * 283
79567 = 251 * 317
79771 = 241 * 331
79921 = 229 * 349
79927 = 257 * 311
79969 = 211 * 379
80057 = 223 * 359
80089 = 283 * 283
80131 = 227 * 353
80441 = 257 * 313
80543 = 239 * 337
80741 = 263 * 307
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