Problems & Puzzles:
Puzzles
Puzzle 16.- Consecutive primes and ending digit
Here I’ll keep the earliest "k" consecutive primes of
ending digit "e"
Solution
k |
e=1 |
e=3 |
e=7 |
e=9 |
5 |
216401
216421
216431
216451
216481 |
752023
752033
752053
752083
752093 |
192637
192667
192677
192697
192737 |
123229
123239
123259
123269
123289 |
6 |
2229971 2229991
2230001 2230021 2230051 2230061 |
2707163 2707183
2707213 2707223 2707273 2707283 |
776257 776267
776287 776317 776327 776357 |
2134519 2134529
2134549 2134579 2134589 2134609 |
7 |
3873011
3873041 3873061 3873071 3873091 3873101 3873151 |
44923183
44923213 44923223 44923253 44923273 44923283 44923303 |
15328637
15328657 15328667 15328697 15328717 15328727 15328757 |
12130109
12130159 12130169 12130259 12130289 12130309 12130319 |
8 |
36539311
36539381 36539401 36539411
36539431 36539441 36539471 36539491 |
44923183
44923213 44923223 44923253
44923273 44923283 44923303 44923313 |
70275277
70275307 70275347 70275367
70275377 70275397 70275407 70275427 |
23884639
23884669 23884699 23884709
23884739 23884759 23884769 23884799 |
9 |
36539311
36539381 36539401 36539411 36539431
36539441 36539471 36539491 36539501 |
961129823
961129843 961129853 961129903 961129933
961129943 961129963 961129973 961129993
|
244650317
244650337 244650347 244650377 244650397
244650407 244650437 244650457 244650617
|
363289219
363289229 363289249 363289259 363289309
363289319 363289349 363289369 363289379
|
10 |
196943081
196943101 196943141 196943161 196943171
196943221 196943231 196943261 196943281
196943291 |
1147752443
1147752493 1147752523 1147752553 1147752583
1147752623 1147752673 1147752713 1147752733
1147752743 |
452942827
452942837 452942857 452942927 452942947
452942977 452943047 452943097 452943107
452943137 |
|
11 |
|
|
452942827 452942837 452942857 452942927
452942947 452942977
452943047 452943097 452943107 452943137
452943157 |
|
All primes for k>5 were sent by Jud McCranie on 16/08/98
More solutions came from Giovanni Resta
(Nov. 2004):
For brevity I have indicated only
the first and last number of the sequence.
K E FIRST LAST
10 1 196943081 ... 196943291
10 3 1147752443 ... 1147752743
10 7 4075366567... 4075366817
10 9 9568590299 ... 9568590529
11 1 14293856441 ... 14293856701
11 3 6879806623 ... 6879806933
11 7 452942827 ... 452943157
11 9 24037796539 ... 24037796789
12 1 363373386721 ... 363373387151
12 3 131145172583 ... 131145172913
12 7 73712513057 ... 73712513627
12 9 130426565719 ... 130426566079
13 1 381206903941 ... 381206904461
13 3 177746482483 ... 177746482853
13 7 319931193737 ... 319931194127
13 9 405033487139 ... 405033487499
14 1 154351758091 ... 154351758551
14 3 795537219143 ... 795537219443
14 7 2618698284817 ... 2618698285337
14 9 3553144754209 ... 3553144754689
15 3 4028596340953 ... 4028596341463
15 9 4010803176619 ... 4010803177049
16 3 6987191424553 ... 6987191425073
***
Jan van Delden wrote on May 4, 2020
I’m busy optimizing my sieve-program, I needed a test, so
my contribution for Puzzle 16:
Ending digit 7 Length: 15 Start prime: 10993283241587
Ending digit 1 Length: 15 Start prime: 11992377039481
Ending digit 1 Length: 16 Start prime: 41947964349971
Ending digit 7 Length: 16 Start prime: 54010894438097
Ending digit 9 Length: 17 Start prime: 71894236537009
Ending digit 9 Length: 16 Start prime: 84826861745009
Ending digit 7 Length: 17
Start prime: 101684513099627
***
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