Xi'an's Og

An arithmetics Le Monde mathematical puzzle:

Find all bi-twin integers, namely positive integers such that adding 2 to any of their dividers returns a prime number.

An easy puzzle, once the R libraries on prime number decomposition can be found!, since it is straightforward to check for solutions. Unfortunately, I could not install the recent numbers package. So I used instead the schoolmath R package. Despite its possible bugs. But it seems to do the job for this problem:

[sourcecode language=”r” gutter=”false”]
lem=NULL
for (t in 1:1e4)
if (prod(is.prim(prime.factor(t)+2)==1))
lem=c(lem,t)digin=function(n){
[/sourcecode]

which returned all solutions, albeit in a lengthy fashion:

[sourcecode language=”r” gutter=”false”]
> lem
[1] 1 3 5 9 11 15 17 25 27 29 33 41 45 51 55
[16] 59 71 75 81 85 87 99 101 107 121 123 125 135 137 145
[31] 149 153 165 177 179 187 191 197 205 213 225 227 239 243 255
[46] 261 269 275 281 289 295 297 303 311 319 321 347 355 363 369
[61] 375 405 411 419 425 431 435 447 451 459 461 493 495 505 521
[76] 531 535 537 561 569 573 591 599 605 615 617 625 639 641 649
[91] 659 675 681 685 697 717 725 729 745 765 781 783 807 809 821
[106] 825 827 841 843 857 867 881 885 891 895 909 933 935 955 957
[121] 963 985 1003 1019 1025 1031 …
[/sourcecode]

This entry was posted on June 12, 2015 at 12:15 am and is filed under Books, Kids, Statistics, University life with tags Le Monde, mathematical puzzle, numbers, packages, prime number, R, schoolmath, twin prime numbers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.