Does having prime neighbors make you more composite? | bit-player

Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal num­bers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thi...

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Hasnain says:

Very interesting analysis of what the author calls “tweens”: the numbers in between twin primes. There’s a lot of interesting patterns that I was not aware of before and it was a nice refresher on some number theory and probability concepts.

“When I first began to ponder the tweens, I went looking to see what other people might have said on the subject. I didn’t find much. Although the literature on twin primes is immense, it focuses on the primes themselves, and especially on the question of whether there are infinitely many twins—a conjecture that’s been pending for 170 years. The numbers sandwiched between the primes are seldom mentioned.

The many varieties of highly composite numbers also have an enthusiastic fan club, but I have found little discussion of their frequent occurrence as neighbors of primes.

Could it be that I’m the first person ever to notice the curious properties of twin tweens? No. I am past the age of entertaining such droll thoughts, even transiently. If I have not found any references, it’s doubtless because I’m not looking in the right places. (Pointers welcome.)”

Posted on 2021-11-05T21:11:53+0000