[seqfan] when is 1234...n a prime?

[Sven Simon]

In the case you use only the digits 0,1,...9 and continue with 0,1,2 again, or without digit 0 too, there are some more primes. You can start with other digits than 1 too. And don't forget to count down 9,8,7, and so on. When you use digits only the numbers do not grow that quickly, so you have more chances to find a prime of small size. I am quite sure, that the occurrence of these numbers can be estimated well using statistics. They  just happen sometimes, if you search enough. 

So if you  want to use the continuation 10,11,12,13,14,15 you can start with other numbers than 1 to generate more chances for primes.

But with digits, there seems to be an effect, that there are  less primes counting down, which I cannot explain.

The larger primes are no proven primes, just tested (long ago, when I was more interested in base dependant numbers). Some primes tested again with Pari say these are primes. 

Counting down, mixed with and without 0
43,109,1987,10987,76543

19876543219876543219876543219876543219876543
10987654321098765432109876543210987
4321098765432109876543210987654321098765432109876543210987654321

Counting up, mixed with and without 0
23,67,89,4567,67891,78901,89123,678901,4567891,23456789,45678901,
56789123,1234567891,4567891234567,9012345678901,789012345678901,890123456789123

Without 0
1234567891234567891234567891
1234567891234567891234567891234567891234567891234567891234567891234567
23456789123456789
23456789123456789123
23456789123456789123456789123456789123
23456789123456789123456789123456789123456789123456789123456789
4567891234567891234567891
4567891234567891234567891234567891234567891234567891234567891
56789123456789123456789123456789123456789123
56789123456789123456789123456789123456789123456789123456789
67891234567891234567891234567891234567891
7891234567891234567891234567891
91234567891234567

With 0
2345678901234567890123456789012345678901234567890123456789012345678901234567890123
56789012345678901234567890123
678901234567890123456789012345678901
789012345678901234567890123456789012345678901234567
8901234567890123456789012345678901234567890123456789012345678901234567890123456789
90123456789012345678901234567
9012345678901234567890123456789012345678901

Sven


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