| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
This is really a set, not a sequence: 2, 3, 5, 7, 11, 13, 17, 37, 79, 101, 107, 113, 131, ... Can you tell what some more elements are? How many elements do you suppose there are in the set? John
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 988.1 | CLT::GILBERT | Multiple inheritence happens | Fri Dec 09 1988 20:21 | 3 | |
Let me guess. These are primes p for which reverse(p) is also prime and reverse(p) >= p, where reverse(x) is the value of the decimal digit reversal of x. If so, 149 and 151 are the next values in the series. | |||||
| 988.2 | .1 | VINO::JMUNZER | Mon Dec 12 1988 18:54 | 6 | |
Peter:
Right. And Dan has interesting things to say about how many of these
there are.
John
| |||||
| 988.3 | maybe there are "sagans and sagans" of them :-) | AITG::DERAMO | Daniel V. {AITG,ZFC}:: D'Eramo | Tue Dec 13 1988 02:11 | 31 |
The set described in .0 contains all primes of the forms:
111...11, i.e., all one's in decimal, or (10^n - 1)/9
100...01, i.e., one more than a power of ten, or 10^n + 1
Primes of either form are discussed in other notes in this
file (both are palindromic primes; the first are called
repunits; so DIR/TITLE=PALIND or DIR/TITLE=REPUNIT may find
them, but I haven't checked that). For (10^n - 1)/9 to be
prime, n must be prime. For 10^n + 1 to be prime, n must be
a power of two. In a sense these are the base ten analogs
of the Mersenne primes and the Fermat primes.
>> .0 How many elements do you suppose there are in the set?
>> .2 Right. And Dan has interesting things to say about how many
>> of these there are.
To the best of my knowledge, it is an open problem whether
there are finitely many or infinitely many of either of
these very restricted types of primes (which are a subset of
the palindromic primes, which are a subset of the "forward-
and-backward" primes of .0).
On the other hand, I think only four or five primes of the
first type are known, and certainly even fewer of the
second.
Dan
| |||||