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I was looking for some properties of the prime numbers, and I found some curiosities of the number 17 in that site.

One of them is this

17 was called by the Pythagoreans - opposition, obstruction, and evil, and the day the Devil triumphed over God.

But, unlike the other curiosities, it has no reference. Have you read anything like that? Can you tell me more about this?

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  • $\begingroup$ Welcome. Something like that appears in Plutarch "Pythagoreans call this day [the17th] "the Barrier," and utterly abominate this number": (link(s)&more in wikipedia at 17(number) ). $\endgroup$
    – sand1
    Oct 13, 2018 at 17:24
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    $\begingroup$ Pythagoreans lived around 6-4th century BC in Greece, for them there was no God, only gods, and most certainly no Devil. Curiously, there is a mathematical sense in which 17 was "the barrier", "In Plato's Theaetetus we learn that mathematician Theodorus has established irrationality of square roots for all non-square numbers up to 17 and then he stopped", see Why 17? on Cut the Knot. $\endgroup$
    – Conifold
    Oct 13, 2018 at 19:12
  • $\begingroup$ Some details in R.Laroche, Popular Symbolic/Mystical Numbers in Antiquity (1995). $\endgroup$
    – Mauro ALLEGRANZA
    Oct 13, 2018 at 20:50
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    $\begingroup$ It's a well-known fact that 17 is the world's most random number. You could look it up. :-) $\endgroup$
    – Carl Witthoft
    Oct 15, 2018 at 12:58
  • $\begingroup$ 18 devided by 17 has been used as a value for the half tone in music $\endgroup$
    – John Shanahan
    Apr 13, 2020 at 11:17

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See page 97 of The Mathematical Experience by Davis and Hersh for an explanation of why the Pythagoreans abominated the number 17. There it says Plutarch wrote that the Egyptians related that the death of Osiris occurred on the seventeenth of the month, when the full moon is most obviously waning. Also, the number seventeen is between the two numbers (sixteen and eighteen) that can be simultaneously perimeters and areas of rectangles (sides 4 and 4 or 3 and 6).

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17 is apparently "the barrier" firstly b/c it comes between 16, relating to a square, and 18, which relates to a rectangle, and secondly because it separates 18 from it's epogdoon 16, the number with which it has the relationship 9:8, the major second (loosely speaking / usually). IDK why the Pythagoreans "abominated" 17; they loved 153, the triangle of 17. (-Perhaps it is partly because of the extremely dissonant nature of the major second interval (or so it was considered until relatively recently, early last century or so)?)

17 is the number of consonants in the classical Greek alphabet; I'm aware of the linking of various entities (elements, stars, planets, etc.) to the letters, but cannot personally evaluate claims of historical religious significance related to isopsephy/gematria - though I'd like to think that the Cambridge School will be vindicated) 😄. ...Perhaps someone with better qualifications can weigh in?

I'm sorry I can't give refs; my notes from that period are sadly incomplete.

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