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 2018-12-14, 05:45 #34 enzocreti   Mar 2018 17·31 Posts unusual No this is not unusual i agree... anyway the multiples of 215 and 36, that are unusual
2018-12-14, 06:36   #35
CRGreathouse

Aug 2006

3·1,987 Posts

Quote:
 Originally Posted by enzocreti anyway the multiples of 215 and 36, that are unusual
OK. But order is important, you found the numbers first, then discovered that there were multiples of those numbers -- you didn't say that you expected to find multiples of 215 and 36, and then start calculating. So we shouldn't look at the chance that you'd find three multiples of 215 and two multiples of 36, but rather some number of multiples around that size. Can you think of a good model to check, and then decide what the odds are for that model? That way we can see if what happened here is, in fact, unusual.

2018-12-14, 07:23   #36
enzocreti

Mar 2018

17×31 Posts
I CANT

Quote:
 Originally Posted by CRGreathouse OK. But order is important, you found the numbers first, then discovered that there were multiples of those numbers -- you didn't say that you expected to find multiples of 215 and 36, and then start calculating. So we shouldn't look at the chance that you'd find three multiples of 215 and two multiples of 36, but rather some number of multiples around that size. Can you think of a good model to check, and then decide what the odds are for that model? That way we can see if what happened here is, in fact, unusual.

NO I cant I am not Andrew Wiles!!!

2018-12-14, 07:37   #37
CRGreathouse

Aug 2006

596110 Posts

Quote:
 Originally Posted by enzocreti NO I cant I am not Andrew Wiles!!!
Let's start with something more basic. Given a random integer*, what is the probability that it is divisible by 36? Given 37 random integers, what is the probability that at least 2 are divisible by 36?

* There is a technical problem here -- there is no uniform distribution over the integers -- but it can be avoided so I'll just handwave for now.

Last fiddled with by CRGreathouse on 2018-12-14 at 07:38

 2018-12-14, 09:37 #38 enzocreti   Mar 2018 17×31 Posts probability I don't know, I think anyway it is a low chance and even lower ,given 37 random numbers, the chance three numbers are divisible by 215 Last fiddled with by enzocreti on 2018-12-14 at 09:39
 2018-12-14, 10:23 #39 enzocreti   Mar 2018 17·31 Posts 215 moreover: pg(215) is prime pg(215*428) is prime pg(215*324) is prime. 428 and 324 are both congruent to -1 mod 13.
 2018-12-14, 10:33 #40 enzocreti   Mar 2018 17·31 Posts 215 Moreover: 215 is congruent to 111 mod 13 215*428 is congruent to -111 mod 13 215*324 is congruent to -111 mod 13
 2018-12-14, 10:58 #41 enzocreti   Mar 2018 17×31 Posts 215* Moreover: 215 is congruent to -(2^3-1) mod 111 215*324 is congruent to (2^6-1) mod 111 215*428 is congruent to (2^1-1) mod 111
 2018-12-14, 12:23 #42 enzocreti   Mar 2018 17·31 Posts 215 I don't know if this is redundant: 215 is congruent to 7 mod 13 (215*324) is congruent to - 7 mod 13 (215*428) is congruent to -7 mod 13
 2018-12-14, 12:24 #43 enzocreti   Mar 2018 10000011112 Posts coincidence If all these are coincidences, I am superman!
 2018-12-14, 12:52 #44 enzocreti   Mar 2018 17×31 Posts pg(43k) if you extend to the pg(43k) in the case pg(541456) is prime and 541456 is congruent to -111 mod 13 Last fiddled with by enzocreti on 2018-12-14 at 12:55

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