How many primes below 300 are followed
by a semiprime number?
List them.
There are 9 such prime-semiprime pairs below 300--the top part of the below list. Each line of the list shows the prime and the semiprime, after which is shown the prime factorization of the semiprime. The list is continued up through the 300th such pair. Of course all these semiprimes are even and so have 2 as one of the factors.
3 4 2 * 2
5 6 2 * 3
13 14 2 * 7
37 38 2 * 19
61 62 2 * 31
73 74 2 * 37
157 158 2 * 79
193 194 2 * 97
277 278 2 * 139
---------9
313 314 2 * 157
397 398 2 * 199
421 422 2 * 211
457 458 2 * 229
541 542 2 * 271
613 614 2 * 307
661 662 2 * 331
673 674 2 * 337
733 734 2 * 367
757 758 2 * 379
877 878 2 * 439
997 998 2 * 499
1093 1094 2 * 547
1153 1154 2 * 577
1201 1202 2 * 601
1213 1214 2 * 607
1237 1238 2 * 619
1321 1322 2 * 661
1381 1382 2 * 691
1453 1454 2 * 727
1621 1622 2 * 811
1657 1658 2 * 829
1753 1754 2 * 877
1873 1874 2 * 937
1933 1934 2 * 967
1993 1994 2 * 997
2017 2018 2 * 1009
2137 2138 2 * 1069
2341 2342 2 * 1171
2473 2474 2 * 1237
2557 2558 2 * 1279
2593 2594 2 * 1297
2797 2798 2 * 1399
2857 2858 2 * 1429
2917 2918 2 * 1459
3061 3062 2 * 1531
3217 3218 2 * 1609
3253 3254 2 * 1627
3313 3314 2 * 1657
3517 3518 2 * 1759
3733 3734 2 * 1867
4021 4022 2 * 2011
4057 4058 2 * 2029
4177 4178 2 * 2089
4261 4262 2 * 2131
4273 4274 2 * 2137
4357 4358 2 * 2179
4441 4442 2 * 2221
4561 4562 2 * 2281
4621 4622 2 * 2311
4933 4934 2 * 2467
5077 5078 2 * 2539
5101 5102 2 * 2551
5113 5114 2 * 2557
5233 5234 2 * 2617
5413 5414 2 * 2707
5437 5438 2 * 2719
5581 5582 2 * 2791
5701 5702 2 * 2851
6037 6038 2 * 3019
6073 6074 2 * 3037
6121 6122 2 * 3061
6133 6134 2 * 3067
6217 6218 2 * 3109
6337 6338 2 * 3169
6361 6362 2 * 3181
6373 6374 2 * 3187
6637 6638 2 * 3319
6661 6662 2 * 3331
6781 6782 2 * 3391
6997 6998 2 * 3499
7057 7058 2 * 3529
7213 7214 2 * 3607
7393 7394 2 * 3697
7417 7418 2 * 3709
7477 7478 2 * 3739
7537 7538 2 * 3769
7753 7754 2 * 3877
7933 7934 2 * 3967
8053 8054 2 * 4027
8101 8102 2 * 4051
8221 8222 2 * 4111
8317 8318 2 * 4159
8353 8354 2 * 4177
8461 8462 2 * 4231
8521 8522 2 * 4261
8677 8678 2 * 4339
8713 8714 2 * 4357
8893 8894 2 * 4447
9013 9014 2 * 4507
9133 9134 2 * 4567
9181 9182 2 * 4591
9241 9242 2 * 4621
9277 9278 2 * 4639
9601 9602 2 * 4801
9661 9662 2 * 4831
9721 9722 2 * 4861
9817 9818 2 * 4909
9901 9902 2 * 4951
9973 9974 2 * 4987
10333 10334 2 * 5167
10357 10358 2 * 5179
10453 10454 2 * 5227
10837 10838 2 * 5419
10861 10862 2 * 5431
10957 10958 2 * 5479
11113 11114 2 * 5557
11161 11162 2 * 5581
11317 11318 2 * 5659
11497 11498 2 * 5749
11677 11678 2 * 5839
11701 11702 2 * 5851
12073 12074 2 * 6037
12157 12158 2 * 6079
12241 12242 2 * 6121
12301 12302 2 * 6151
12421 12422 2 * 6211
12433 12434 2 * 6217
12457 12458 2 * 6229
12541 12542 2 * 6271
12553 12554 2 * 6277
12601 12602 2 * 6301
12721 12722 2 * 6361
12757 12758 2 * 6379
12841 12842 2 * 6421
12853 12854 2 * 6427
13093 13094 2 * 6547
13381 13382 2 * 6691
13417 13418 2 * 6709
13681 13682 2 * 6841
13921 13922 2 * 6961
13933 13934 2 * 6967
14437 14438 2 * 7219
14593 14594 2 * 7297
14737 14738 2 * 7369
14821 14822 2 * 7411
15013 15014 2 * 7507
15073 15074 2 * 7537
15121 15122 2 * 7561
15241 15242 2 * 7621
15277 15278 2 * 7639
15361 15362 2 * 7681
15373 15374 2 * 7687
15733 15734 2 * 7867
15901 15902 2 * 7951
16033 16034 2 * 8017
16333 16334 2 * 8167
16381 16382 2 * 8191
16417 16418 2 * 8209
16573 16574 2 * 8287
16633 16634 2 * 8317
16657 16658 2 * 8329
16921 16922 2 * 8461
17041 17042 2 * 8521
17053 17054 2 * 8527
17077 17078 2 * 8539
17257 17258 2 * 8629
17293 17294 2 * 8647
17377 17378 2 * 8689
17881 17882 2 * 8941
18013 18014 2 * 9007
18097 18098 2 * 9049
18133 18134 2 * 9067
18181 18182 2 * 9091
18217 18218 2 * 9109
18253 18254 2 * 9127
18301 18302 2 * 9151
18313 18314 2 * 9157
18397 18398 2 * 9199
18481 18482 2 * 9241
18553 18554 2 * 9277
18637 18638 2 * 9319
18793 18794 2 * 9397
19237 19238 2 * 9619
19441 19442 2 * 9721
19477 19478 2 * 9739
19717 19718 2 * 9859
19801 19802 2 * 9901
19813 19814 2 * 9907
19861 19862 2 * 9931
20353 20354 2 * 10177
20533 20534 2 * 10267
20641 20642 2 * 10321
20857 20858 2 * 10429
21001 21002 2 * 10501
21061 21062 2 * 10531
21193 21194 2 * 10597
21277 21278 2 * 10639
21313 21314 2 * 10657
21577 21578 2 * 10789
21661 21662 2 * 10831
21673 21674 2 * 10837
21817 21818 2 * 10909
22093 22094 2 * 11047
22501 22502 2 * 11251
22573 22574 2 * 11287
22621 22622 2 * 11311
22993 22994 2 * 11497
23053 23054 2 * 11527
23173 23174 2 * 11587
23557 23558 2 * 11779
23677 23678 2 * 11839
23773 23774 2 * 11887
23917 23918 2 * 11959
24097 24098 2 * 12049
24421 24422 2 * 12211
24481 24482 2 * 12241
24781 24782 2 * 12391
24841 24842 2 * 12421
25033 25034 2 * 12517
25153 25154 2 * 12577
25237 25238 2 * 12619
25561 25562 2 * 12781
25657 25658 2 * 12829
25933 25934 2 * 12967
26017 26018 2 * 13009
26293 26294 2 * 13147
26317 26318 2 * 13159
26437 26438 2 * 13219
26497 26498 2 * 13249
26821 26822 2 * 13411
26833 26834 2 * 13417
26881 26882 2 * 13441
26953 26954 2 * 13477
27073 27074 2 * 13537
27253 27254 2 * 13627
27337 27338 2 * 13669
27361 27362 2 * 13681
27457 27458 2 * 13729
27997 27998 2 * 13999
28057 28058 2 * 14029
28297 28298 2 * 14149
28393 28394 2 * 14197
28813 28814 2 * 14407
28837 28838 2 * 14419
28921 28922 2 * 14461
29101 29102 2 * 14551
29473 29474 2 * 14737
29641 29642 2 * 14821
30181 30182 2 * 15091
30241 30242 2 * 15121
30517 30518 2 * 15259
30553 30554 2 * 15277
30577 30578 2 * 15289
30637 30638 2 * 15319
30661 30662 2 * 15331
30697 30698 2 * 15349
30781 30782 2 * 15391
30853 30854 2 * 15427
31081 31082 2 * 15541
31237 31238 2 * 15619
31321 31322 2 * 15661
31333 31334 2 * 15667
31357 31358 2 * 15679
31477 31478 2 * 15739
31573 31574 2 * 15787
31873 31874 2 * 15937
31981 31982 2 * 15991
32173 32174 2 * 16087
32377 32378 2 * 16189
32497 32498 2 * 16249
32533 32534 2 * 16267
32833 32834 2 * 16417
33037 33038 2 * 16519
33301 33302 2 * 16651
33457 33458 2 * 16729
33493 33494 2 * 16747
33757 33758 2 * 16879
33961 33962 2 * 16981
34057 34058 2 * 17029
34213 34214 2 * 17107
34273 34274 2 * 17137
34381 34382 2 * 17191
34513 34514 2 * 17257
34897 34898 2 * 17449
34981 34982 2 * 17491
35317 35318 2 * 17659
35521 35522 2 * 17761
35677 35678 2 * 17839
35977 35978 2 * 17989
36097 36098 2 * 18049
36241 36242 2 * 18121
36433 36434 2 * 18217
36457 36458 2 * 18229
36793 36794 2 * 18397
36877 36878 2 * 18439
36901 36902 2 * 18451
36913 36914 2 * 18457
37273 37274 2 * 18637
37321 37322 2 * 18661
37357 37358 2 * 18679
The program merely had to check if the quotient of the successor number divided by 2 was prime:
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
p = 2
Do
p = nxtprm(p)
If p > 300 And flag = 0 Then Text1.Text = Text1.Text & "---------" & ct & crlf & crlf: flag = 1
sp = p + 1
p2 = sp / 2
If prmdiv(p2) = p2 Then
Text1.Text = Text1.Text & p & Str(sp)
Text1.Text = Text1.Text & " 2 * " & p2 & crlf: ct = ct + 1
End If
DoEvents
Loop Until ct >= 300
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
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Posted by Charlie
on 2019-06-12 12:12:48 |
computer solution
