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Old 2008-04-24, 17:23   #1
davar55
 
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Default 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 ?
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Old 2008-04-24, 18:28   #2
petrw1
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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
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Old 2009-07-06, 02:43   #3
davar55
 
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What about my other question?
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Old 2009-07-19, 04:23   #4
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Quote:
Originally Posted by davar55 View Post
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
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Old 2009-07-19, 17:21   #5
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Quote:
Originally Posted by Mr. P-1 View Post
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.
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Old 2009-07-19, 17:50   #6
10metreh
 
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Quote:
Originally Posted by lavalamp View Post
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
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Old 2009-07-19, 19:53   #7
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Meh, I just copied Mr. P-1 and slightly edited the start. ;)
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Old 2009-07-20, 00:11   #8
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Quote:
Originally Posted by lavalamp View Post
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
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Old 2010-12-20, 12:39   #9
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So far the list is:

1 -> 10123457689

2 -> 100112233445566877989

3 -> ?????

How far can we extend this?
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Old 2010-12-21, 11:54   #10
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1012345768.9999...
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Old 2010-12-22, 05:01   #11
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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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