# 2013 is the first of a sphenic triplet

A sphenic number is the product of three distinct prime numbers. The lowest sphenic numbers are:

30 = 2 x 3 x 5
42 = 2 x 3 x 7
66 = 2 x 3 x 11
70 = 2 x 5 x 7

If two consecutive numbers are both sphenic, they are called sphenic twins:

230 = 2 x 5 x 23
231 = 3 x 7 x 11

285 = 3 x 5 x 19
286 = 2 x 11 x 13

429 = 3 x 11 x 13
430 = 2 x 5 x 43

I have not seen the phrase used anywhere, but it seems to me that a series of three consecutive sphenic numbers ought to be called sphenic triplets. 2013 is the first of the third lowest set of sphenic triplets.

1309 = 7 x 11 x 17
1310 = 2 x 5 x 131
1311 = 3 x 19 x 23

1885 = 5 x 13 x 29
1886 = 2 x 23 x 41
1887 = 3 x 17 x 37

2013 = 3 x 11 x 61
2014 = 2 x 19 x 53
2015 = 5 x 13 x 31

I have not calculated the next sphenic triplets; the above is quite enough.

I suppose that there must be an infinite number of sphenic triplets; I cannot see why there should be an upper limit.

It is impossible to have four consecutive sphenic numbers, because every fourth number is divisible by four and therefore cannot be sphenic.

So how is your morning going? My train is running late and I will certainly miss my connection.

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