ron@ada-uts.UUCP (05/14/85)
"The set of all primes p such that 10p + r (r = 1,3,7,9) is also in the set for some r." This definition doesn't make any sense at all. I also don't see an obvious way to turn it into a description of the set in question.
tower@inmet.UUCP (05/15/85)
> /**** inmet:net.math / ihnet!eklhad / 9:33 am May 7, 1985 ****/ > How many primes, when written in base 10, > also produce prime sub-numbers (looking at the first n digits)? > For example: 7193 is in the set, since > 7, 71, 719, and 7193 are all prime. > The list begins: 3, 5, 7, 31, 37, 53, 59, 71, 73, 79, > 311, 313, 317, 373, 379, 593, 599, ... > Is the list infinite? > If so, can anyone prove it. > If not, and I conjecture not, what is the largest such number? > Anyone with some time (personal and computer) can enjoy this one. > Karl Dahlke ihnp4!ihnet!eklhad Ok, now that we're looking at base 10, lets generalise the problem: For what bases is the list (defined above) for that base infinite? -len tower UUCP: {bellcore,ihnp4}!inmet!tower Intermetrics, Inc. INTERNET: ima!inmet!tower@CCA-UNIX.ARPA USPS: 733 Concord Ave., Cambridge, MA 02138, USA PHONE: (617) 661-1840
phil@mirror.UUCP (05/15/85)
/**** mirror:net.math / faron!bs / 8:43 am May 10, 1985 ****/
>
The set is quite definitely finite. In fact it is rather small and takes
very little computer time to generate. A better way of defining it is:
The set of all primes p such that 10p + r (r = 1,3,7,9) is also in the
set for some r.
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Your set is ill-defined. Consider the largest number P' of your
'finite' set. P' is in the set iff some larger number is also in the
set.