Problems & Puzzles:
Puzzles
Puzzle
578.-
The smallest prime
concatenating the first k primes
Here I ask for the smalllest prime
concatenating the first k primes:
Here are the smallest prime up to k=6
|
k |
smallest prime |
|
1 |
2 |
|
2 |
23 |
|
3 |
523 |
|
4 |
2357 |
|
5 |
112573 |
|
6 |
11132357 |
Q1. Can you extend
this table?
Q2. For a similar but non equal question see
A083427. Can you extend this other table?
Wow! This became a very popular puzzle!
Contributions came from: Jean Brette, Torbjörn Alm,
Robert D. Mohr, Jan van Delden, Farid Liam, Seiji Tomita, J-C Rosa,
Emmanuel Vantieghem, Hakan Summakoglu, Farideh Firoozbalht & J. K.
Andersen.
***
For Q1 here are the solutions & Puzzlers involved.
Every puzzlers is named until his last correct entry, no
matter if after his first mistake he sent other correct entries.
|
k & smallest prime |
Puzzlers |
|
7 1113257317 |
TA, FL, JC, EV, HS, FF, JKA, RM, JVD |
|
8 111317193257 |
TA, FL, JC, EV, HS, FF, JKA, RM, JVD |
|
9 11131719223357 |
TA, FL, JC, EV, HS, FF, JKA, RM, JVD |
|
10 none |
|
|
11 111317192232935317 |
TA, FL, JC, HS, FF, JKA, RM, JVD |
|
12 11131719223293157373 |
FL, HS, FF, JKA, RM, JVD |
|
13 1113171922329313377541 |
FL, HS, FF, JKA, RM, JVD |
|
14 111317192232931337415743 |
FL, HS, FF, JKA, RM, JVD |
|
15 11131719223293133741474357 |
HS, FF, JKA, RM, JVD |
|
16 none |
|
|
17 111317192232931337414355975347 |
HS, FF, JKA, RM, JVD |
|
18 none |
|
|
19 1113171922329313374143475357596167 |
HS, FF, JKA, RM, JVD |
|
20 none |
|
|
21 11131719223293133741434753559677376171 |
HS, JKA, RM, JVD |
|
22 1113171922329313374143475355961677973771 |
HS, JKA, RM, JVD |
|
23 111317192232931337414347535596167718373779 |
HS, JKA, RM, JVD |
|
24 none |
|
|
25 1113171922329313374143475355961677173779898397 |
HS, JKA, RM, JVD |
|
26 none |
|
|
27 1011031113171922329313374143475355961677173837899779 |
JKA, JVD |
|
28 none |
|
|
29 1011031071091113171922329313374143475355961677173797798983 |
JKA, JVD |
For Q2:
|
Primes |
Puzzlers |
|
n=9 11131719223357 |
HS, FF, EV |
|
n=10 1113171922335437 |
HS, FF, EV |
|
n=11 111317192232934157 |
HS, FF, EV |
|
n=12 11131719223293135773 |
HS, FF |
|
n=13 1113171922329313375759 |
HS, FF |
|
n=14 111317192232931337415743 |
HS, FF |
|
n=15 11131719223293133741435717 |
HS, FF |
|
n=16 1113171922329313374143477357 |
HS, FF |
|
n=17 111317192232931337414347559783 |
HS |
|
n=18 11131719223293133741434753578371 |
HS |
|
n=19 1113171922329313374143475355961789 |
HS |
|
n=20 111317192232931337414347535596173797 |
HS |
|
n=21 11131719223293133741434753559616771783 |
HS |
|
n=22 1113171922329313374143475355961677197779 |
HS |
|
n=23 111317192232931337414347535596167717389779 |
HS |
|
n=24 11131719223293133741434753559616771797389977 |
HS |
|
n=25 1113171922329313374143475355961677173779898397 |
HS |
|
