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 2008-04-24, 17:23 #1 davar55     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 ?
 2008-04-24, 18:28 #2 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 43·107 Posts Must have at least 11 digits ... and combination of exactly one 0-9 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 2008-04-24 at 18:29
 2009-07-06, 02:43 #3 davar55     May 2004 New York City 3×17×83 Posts What about my other question?
2009-07-19, 04:23   #4
Mr. P-1

Jun 2003

7×167 Posts

Quote:
 Originally Posted by davar55 What about my other question?
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. P-1 on 2009-07-19 at 04:24

2009-07-19, 17:21   #5
lavalamp

Oct 2007
Manchester, UK

17×79 Posts

Quote:
 Originally Posted by Mr. P-1 The same reasoning leads to the conclusion that 1001122334455667799 is the lowest possible answer, though not prime
If the requirement that it be prime is waived, the smallest such number is 100122334455667799.

2009-07-19, 17:50   #6
10metreh

Nov 2008

2×33×43 Posts

Quote:
 Originally Posted by lavalamp If the requirement that it be prime is waived, the smallest such number is 100122334455667799.
What happened to 8?

BTW, the smallest that is a prime (including the 8) is 100112233445566877989

Last fiddled with by 10metreh on 2009-07-19 at 18:03

 2009-07-19, 19:53 #7 lavalamp     Oct 2007 Manchester, UK 101001111112 Posts Meh, I just copied Mr. P-1 and slightly edited the start. ;)
2009-07-20, 00:11   #8
Mr. P-1

Jun 2003

7×167 Posts

Quote:
 Originally Posted by lavalamp If the requirement that it be prime is waived, the smallest such number is 10012233445566778899.
8s reinst8ed.

The number I gave adhered to the requirement that it was not a multiple of 3.

Last fiddled with by Mr. P-1 on 2009-07-20 at 00:12

 2010-12-20, 12:39 #9 davar55     May 2004 New York City 10000100010012 Posts So far the list is: 1 -> 10123457689 2 -> 100112233445566877989 3 -> ????? How far can we extend this?
 2010-12-21, 11:54 #10 Mr. P-1     Jun 2003 116910 Posts 1012345768.9999...
 2010-12-22, 05:01 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100100101100112 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 2010-12-22 at 05:59 Reason: 4... 5... 6... 7... 8... 9... 10th is funny :-) 12...

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