20080424, 17:23  #1 
May 2004
New York City
3×17×83 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
43·107 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
3×17×83 Posts 
What about my other question?

20090719, 04:23  #4 
Jun 2003
7×167 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
17×79 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
10100111111_{2} 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
1000010001001_{2} Posts 
So far the list is:
1 > 10123457689 2 > 100112233445566877989 3 > ????? How far can we extend this? 
20101221, 11:54  #10 
Jun 2003
1169_{10} Posts 
1012345768.9999...

20101222, 05:01  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010010110011_{2} 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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