A110600 Minimal set of prime-strings in base 12 in the sense of A071062.

2, 3, 5, 7, 11, 13, 73, 97, 109, 577, 1489, 7537, 17401, 226201, 1097113, 32555521, 388177921

Offset: 1

Author

Walter Kehowski, Sep 14 2005

Keywords

• nonn
• base

Comments

Maple worksheet available upon request. Here is the minimal set in base 12 where X is 10 and E is 11. 2, 3, 5, 7, E, 11, 61, 81, 91, 401, X41, 4441, X0X1, XXXX1, 44XXX1, XXX0001, XX000001. This minimal set demonstrates the elegance of base 12 generally since you can mentally follow the process of elimination, all primes after E end in the neutral digit 1 and the last two entries only contain X, 0 and 1. There are no primes of the form X0...01 since the sum of its digits is E and hence it is divisible by E.

The smallest prime found to date that satisfies all patterns in the minimal set is 1234456789X04XXX00E0001 (656969693573113867991809 in base 10). [Walter Kehowski, May 18 2012]

Examples

			a(10)=401 since no earlier prime in the list contained the pattern "*4*0*1*" where "*" stands for zero or more digits. The list can be manually constructed using a sieve-like process: eliminate all subsequent primes of the form "*4*0*1*" from the list of all primes. Assuming all previous elements have also been similarly determined, the next remaining prime should be X41.
		

Crossrefs

Cf. A071062, A071070.