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

    It looks to me like they get more frequent as you go up; I’ve seen lots of adjacent pairs of triplets go past, and even the occasional adjacent triple of triplets:

    9000000000040781 = 15359 x 477229 x 1227871
    9000000000040782 = 2 x 3 x 253823
    9000000000040783 = 421 x 911 x 9871

    9000000000040785 = 3 x 5 x 103
    9000000000040786 = 2 x 11 x 41
    9000000000040787 = 31 x 157 x 173

    9000000000040789 = 257 x 12227 x 2864108551
    9000000000040790 = 2 x 5 x 13
    9000000000040791 = 3 x 7 x 16267007

    (I’m only looking at ranges just above round numbers, because my lifespan is finite)

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