| 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 |
Let R(n) denote the number whose decimal representation consists of n consecutive 1's. Such a number is called a repunit. It has just been discovered (July 1, 1985) that R(1031) is a prime. This is the largest known repunit prime. Other known repunit primes are: R(2), R(19), R(23), and R(317). [Info from Journal of Recreational Mathematics, vol 18, no. 1, pp 45-46.]
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 378.1 | CESSNA::REILLY | Mon Nov 18 1985 13:37 | 44 | ||
Aren't prime numbers of the form
n
2 - 1
called merseine primes? (I know I'm not even close on the spelling.)
I seem to recall that current thinking points to ALL perfect numbers
(the sum of whose factors, including 1 and excluding the number itself,
equals the number in question) take the form
n-1 n
p = 2 (2 - 1)
Did the authors who announced this "repunit prime" also indicate that they
have thus found the largest perfect number?
(There is a rather simple proof that such numbers are perfect, but it's
not real exciting, so it is after the <FF>.)
Note that another way of stating the definition of a perfect number is
to say that the sum of ALL of its factors equal twice the number itself:
Sum(factors of P) = 2 * P
n-1 n
For P = 2 (2 - 1)
n-1 n
Sum(factors of P) = Sum(factors of 2 (2 -1)) =
n n-1
2 * Sum(factors of 2 ) =
n i
2 * Sum(2 for all i: 0 <= i <= n - 1) =
n n
2 * (2 - 1) = 2 * P
(I've been waiting for an opportunity to work this into a conversation for
a while now....)
matt
| |||||
| 378.2 | BEING::POSTPISCHIL | Mon Nov 18 1985 15:31 | 6 | ||
Re .1: R(n) is a number represented as a string of one's in decimal, not binary. -- edp | |||||
| 378.3 | PIPER::REILLY | Mon Nov 18 1985 17:27 | 6 | ||
oh, well, never mind then.... (I'm sooooo embarassed...) matt | |||||