mersenne {numbers} | R Documentation |
Mersenne Numbers
Description
Determines whether p
is a Mersenne number, that is such that
2^p - 1
is prime.
Usage
mersenne(p)
Arguments
p |
prime number, not very large. |
Details
Applies the Lucas-Lehmer test on p
. Because intermediate numbers will
soon get very large, uses ‘gmp’ from the beginning.
Value
Returns TRUE or FALSE, indicating whether p
is a Mersenne number or not.
References
https://mathworld.wolfram.com/Lucas-LehmerTest.html
Examples
mersenne(2)
## Not run:
P <- Primes(32)
M <- c()
for (p in P)
if (mersenne(p)) M <- c(M, p)
# Next Mersenne numpers with primes are 521 and 607 (below 1200)
M # 2 3 5 7 13 17 19 31 61 89 107
gmp::as.bigz(2)^M - 1 # 3 7 31 127 8191 131071 ...
## End(Not run)
[Package numbers version 0.8-5 Index]