;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]]