20080424, 17:23  #1 
May 2004
New York City
2^{3}×23^{2} Posts 
Multiply Pandigital
Find the smallest prime number whose decimal representation
contains each of the ten digits 0 thru 9 (at least) once. Twice? Three times? Four times? More? How many minimum length (singly) pandigital primes are there in each base b, 2 <= b <= 10 ? 
20080424, 18:28  #2 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2·3^{2}·11·23 Posts 
Must have at least 11 digits ... and combination of exactly one 09 divides 3. Adding zero's doesn't help.
So lowest possible answer is 10123456789. It is not a prime but this is: 10123457689 This is similar (but not identical) to this Project Euler problem: http://projecteuler.net/index.php?se...problems&id=41 Last fiddled with by petrw1 on 20080424 at 18:29 
20090706, 02:43  #3 
May 2004
New York City
4232_{10} Posts 
What about my other question?

20090719, 04:23  #4 
Jun 2003
10010010001_{2} Posts 
The same reasoning leads to the conclusion that 1001122334455667799 is the lowest possible answer, though not prime.
producing a numerically ordered list of permutations and testing each one for primality would be trivial. Last fiddled with by Mr. P1 on 20090719 at 04:24 
20090719, 17:21  #5 
Oct 2007
Manchester, UK
1341_{10} Posts 

20090719, 17:50  #6  
Nov 2008
2·3^{3}·43 Posts 
Quote:
BTW, the smallest that is a prime (including the 8) is 100112233445566877989 Last fiddled with by 10metreh on 20090719 at 18:03 

20090719, 19:53  #7 
Oct 2007
Manchester, UK
3^{2}·149 Posts 
Meh, I just copied Mr. P1 and slightly edited the start. ;)

20090720, 00:11  #8  
Jun 2003
7×167 Posts 
Quote:
The number I gave adhered to the requirement that it was not a multiple of 3. Last fiddled with by Mr. P1 on 20090720 at 00:12 

20101220, 12:39  #9 
May 2004
New York City
2^{3}·23^{2} Posts 
So far the list is:
1 > 10123457689 2 > 100112233445566877989 3 > ????? How far can we extend this? 
20101221, 11:54  #10 
Jun 2003
7×167 Posts 
1012345768.9999...

20101222, 05:01  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}×2,333 Posts 
Code:
3 > 1000111222333444555666778978989 4 > 10000111122223333444455556666777798889989 5 > 100000111112222233333444445555566666777778989998889 6 > 1000000111111222222333333444444555555666666777777888898999899 7 > 10000000111111122222223333333444444455555556666666777777788888999898999 8 > 100000000111111112222222233333333444444445555555566666666777777778888889899999989 9 > 1000000000111111111222222222333333333444444444555555555666666666777777777888888889999899999 10> 10000000000111111111122222222223333333333444444444455555555556666666666777777777788888888889999999999 11> 100000000000111111111112222222222233333333333444444444445555555555566666666666777777777778888888899899999898999 12> 1000000000000111111111111222222222222333333333333444444444444555555555555666666666666777777777777888888888899999989999989 Last fiddled with by Batalov on 20101222 at 05:59 Reason: 4... 5... 6... 7... 8... 9... 10th is funny :) 12... 
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