# project euler – problem 47

November 8, 2011
By

(This article was first published on YGC » R, and kindly contributed to R-bloggers)

```The first two consecutive numbers to have two distinct prime factors are:

14 = 2 × 7
15 = 3 × 5

The first three consecutive numbers to have three distinct prime factors are:

644 = 2² × 7 × 23
645 = 3 × 5 × 43
646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?
```
```getFactor <- function(n) {
f <- c()
for ( i in 2:ceiling(sqrt(n/2)))  {
if (n %%i ==0) {
n <- n/i
while(n %% i ==0) {
n <- n/i
}
f <- c(f,i)
if (gmp::isprime(n) !=0) {
f <- c(f,n)
}
}
}
return(unique(f))
}

i <- 4
n <- 10^(i-1)

while(TRUE) {
flag <- 0
for (j in 0:(i-1)) {
f <- getFactor(n+j)
if(length(f) != i)
break
if(any(gmp::isprime(f) == 0))
break
if (j==i-1)
flag <- 1
}
if (j == i-1 && flag==1) {
print(n)
break
}
n <- n+j+1
}```

when i = 2, the program will print 14, and when i = 3, it will print 644.
This program is not hard coded, i can be set to any number to find the number that satisfy the property of problem 47 wanted.

```> system.time(source("Problem47.R"))
 134043
user  system elapsed
43.22    0.00   43.28  ```

#### Related Posts

To leave a comment for the author, please follow the link and comment on their blog: YGC » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)

Click here to close (This popup will not appear again)