 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Some strings attached (Posted on 2010-12-19) Let P(n) be the product of four consecutive integers, starting with n, minus one:
```
P(n) = n* (n+1)* (n+2) *(n+3) - 1.
```

Clearly, P(n) can be either prime or not. e.g. P(1) = 23 is prime and P(2) = 119 = 7*17 is not.

Let us call "kc-tuple" a string of k consecutive values : { n, n+1, n+2, ..., n+k-1} such that : P(n), P(n+1), ... , P(n+k-1) are all prime.

There is a significant number of twins (kc = 2) or triplets (kc = 3) but the quadruplets (kc = 4) are rather sparse, and 5 & 6-tuples even sparser.

1) Find Āthe 1st four examples for kc=2,3,4, ( 5 & 6 optional) .
2) Prove there are no kc-tuples for kc>6.

 No Solution Yet Submitted by Ady TZIDON No Rating Comments: ( You must be logged in to post comments.)
 Subject Author Date answer for kc=5 Daniel 2010-12-21 21:15:51 solution Justin 2010-12-19 16:57:55 Please log in:

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