**For example** 


*3 consecutive primes in arithmetic progression* 



```
3,5,7  distance 2
151,157,163 distance 6

```

*4 consecutive primes in arithmetic progression*



```
251,257,263,269 distance 6
1741,1747,1753,1753 distance 6
76543,76561,76579,76597 distance 18

```

**Are there five consecutive primes in arithmetic progression?**



Are there five consecutive primes in arithmetic progression?
Yes for the lengths you ask for this is known to exist. 


The minimal example is $9843019+ 30 n$ for $n=0,1,2,3,4$ (taken from the page at the end). 


A more common way to phrase this would be to ask about (five) *consecutive* primes in arithmetic progression. 


Indeed, it is conjectured that there are arbitrarily long (finite) arithmetic progressions of consecutive primes, however this is open. (Without the restriction of the primes being consecutive primes this is known by a well-known result of Green and Tao.)


The longest *known* arithmetic progression of consecutive primes has length ten. 


For further details one could start at <http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression> (see the section towards the end on consecutive primes in AP) for record data related to this see <http://users.cybercity.dk/~dsl522332/math/cpap.htm> 


