;Definitions
A '''sphenic number''' is a positive integer that is the product of three distinct prime numbers. More technically it's a square-free 3-almost prime (see Related tasks below).

For the purposes of this task, a '''sphenic triplet''' is a group of three sphenic numbers which are consecutive. 

Note that sphenic quadruplets are not possible because every fourth consecutive positive integer is divisible by 4 (= 2 x 2) and its prime factors would not therefore be distinct.

;Examples
30 (= 2 x 3 x 5) is a sphenic number and is also clearly the first one.

[1309, 1310, 1311] is a sphenic triplet because 1309 (= 7 x 11 x 17), 1310 (= 2 x 5 x 31) and 1311 (= 3 x 19 x 23) are 3 consecutive sphenic numbers.

;Task
Calculate and show here:

1. All sphenic numbers less than 1,000.

2. All sphenic triplets less than 10,000.

;Stretch

3. How many sphenic numbers are there less than 1 million?

4. How many sphenic triplets are there less than 1 million?

5. What is the 200,000th sphenic number and its 3 prime factors?

6. What is the 5,000th sphenic triplet?

Hint: you only need to consider sphenic numbers less than 1 million to answer 5. and 6.

;References

* [[wp:Sphenic_number|Wikipedia: Sphenic number]]
* [[oeis:A007304|OEIS:A007304 - Sphenic numbers]]
* [[oeis:A165936|OEIS:A165936 - Sphenic triplets (in effect)]]

;Related tasks
* [[Almost prime]]
* [[Square-free integers]]
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