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The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?

?View Code RSPLUS
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  n <- 10^4:10^3 prime <- n[gmp::isprime(n) != 0] pl <- lapply(prime,function(i) unlist(strsplit(as.character(i), split="")))   flag <- 0 for (i in seq_along(pl)) { x <- pl[[i]] maxP <- prime[i]   pl <- pl[-i] prime <- prime[-i]   idx <- unlist(lapply(pl, function(i) all(x %in% i) & all(i %in% x))) idx <- which(idx) if (length(idx) >= 2) { sel <- prime[idx] diff <- maxP-sel for (j in 1:length(diff)) { m <- which(diff == 2* diff[j]) if (length(m) >= 1) { minP <- sel[m[length(m)]] midP <- sel[j] flag <- 1 break } } } if(flag) { break } }   ans <- paste(c(minP, midP, maxP), collapse="") print(ans)
> system.time(source("problem49.R")) system.time(source("problem49.R"))
 "296962999629"
user  system elapsed
0.25    0.00    0.25