# 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"))
[1] 134043
user  system elapsed
43.22    0.00   43.28  ```

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