Just read a puzzling fact in Le Monde science leaflet: someone at the “Great Internet Mersenne Prime Search” (GIMPS) just found a prime number with 17 million digits and…it is the 48th prime number of the form 2p-1. Which just means it is an odd number. How odd a remark!!! And how wrong. In fact, the short news item meant that this is a Mersenne number, of the form 2p-1! Another victim of a hasty cut&paste, I presume…
Archive for prime numbers
odd prime numbers
Posted in Books with tags cut and paste, Le Monde, Mersenne numbers, prime numbers, the Great Internet Mersenne Prime Search on February 9, 2013 by xi'anLe Monde puzzle [#6]
Posted in R, Statistics with tags bug, Le Monde, mathematical puzzle, prime numbers, schoolmath on February 18, 2011 by xi'anA simple challenge in Le Monde this week: find the group of four primes such that any sum of three terms in the group is prime and the overall sum is minimised. Here is a quick exploration by simulation, using the schoolmath package (with its imperfections):
[sourcecode language=”r” gutter=”false”]
A=primes(start=1,end=53)[-1]
lengthA=length(A)
res=4*53
for (t in 1:10^4){
B=sample(A,4,prob=1/(1:lengthA))
sto=is.prim(sum(B[-1]))
for (j in 2:4)
sto=sto*is.prim(sum(B[-j]))
if ((sto)&(sum(B)<res)){
res=sum(B)
sol=B}
}
}
[/sourcecode]
providing the solution 5 7 17 19.
A subsidiary question in the same puzzle is whether or not it is possible to find a group of five primes such that any sum of three terms is still prime. Running the above program with the proper substitutions of 4 by 5 does not produce any solution, even when increasing the upper boundary in A. So it is most likely that the answer is no.
bug in schoolmath
Posted in R with tags bug, prime factor decomposition, prime numbers, R, schoolmath on June 14, 2010 by xi'anNeil Gunther has pointed out on his blog that the prime number decomposition R package schoolmath contains mistakes in the function primes, listing 1 as a prime number but also including decomposable numbers like 133 in its list of prime numbers:
> primes(100,140)
[1] 101 107 111 113 123 129 131 137
> primes(50,140)
[1] 51 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 133
[20] 137 139
> is.prim(primes(133)
[1] FALSE
> is.prim(primes(200,300))
[1] FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
[13] TRUE TRUE TRUE TRUE TRUE TRUE
> sum(1-is.prim(primes(1,1000)))
[1] 10
> data(primlist)
> sum(1-is.prim(primlist[1:25000]))
[1] 3309
This is rather annoying and I hope it gets quickly fixed!
schoolmath
Posted in R with tags arithmetics, prime factor decomposition, prime numbers, R on March 7, 2010 by xi'anIn connection with the Le Monde puzzle of last week, I was looking for an R function that would give me the prime factor decomposition of any integer. Such a function exists within the package schoolmath, developped by Joerg Schlarmann and Josef Wienand. It is called prime.factor and it returns the prime factors of any integer:
> prime.factor(2016)
[1] 2 2 2 2 2 3 3 7
> prime.factor(2032)
[1] 2 2 2 2 127
> prime.factor(2031)
[1] 3 677
> prime.factor(2039)
2039 is a prime!
[1] 2039
Warning [06/14/10]! As pointed out in this blog by Neil Gunther, schoolmath contains mistakes in the function primes, listing 1 as a prime number but also including decomposable numbers like 133.
