541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!! - Page 4

enzocreti · 2018-12-14, 05:45

No this is not unusual i agree...
anyway the multiples of 215 and 36, that are unusual

CRGreathouse · 2018-12-14, 06:36

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.

enzocreti · 2018-12-14, 07:23

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!!!

CRGreathouse · 2018-12-14, 07:37

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.

enzocreti · 2018-12-14, 09:37

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

enzocreti · 2018-12-14, 10:23

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.

enzocreti · 2018-12-14, 10:33

Moreover:

215 is congruent to 111 mod 13
215*428 is congruent to -111 mod 13
215*324 is congruent to -111 mod 13

enzocreti · 2018-12-14, 10:58

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

enzocreti · 2018-12-14, 12:23

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

enzocreti · 2018-12-14, 12:24

If all these are coincidences, I am superman!

enzocreti · 2018-12-14, 12:52

if you extend to the pg(43k)

in the case pg(541456) is prime and 541456 is congruent to -111 mod 13

2018-12-14, 05:45	#34
enzocreti Mar 2018 2×5×53 Posts	unusual No this is not unusual i agree... anyway the multiples of 215 and 36, that are unusual

2018-12-14, 09:37	#38
enzocreti Mar 2018 2·5·53 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 2×5×53 Posts	215 moreover: pg(215) is prime pg(215428) is prime pg(215324) is prime. 428 and 324 are both congruent to -1 mod 13.

2018-12-14, 10:33	#40
enzocreti Mar 2018 2×5×53 Posts	215 Moreover: 215 is congruent to 111 mod 13 215428 is congruent to -111 mod 13 215324 is congruent to -111 mod 13

2018-12-14, 10:58	#41
enzocreti Mar 2018 2·5·53 Posts	215* Moreover: 215 is congruent to -(2^3-1) mod 111 215324 is congruent to (2^6-1) mod 111 215428 is congruent to (2^1-1) mod 111

2018-12-14, 12:23	#42
enzocreti Mar 2018 530₁₀ Posts	215 I don't know if this is redundant: 215 is congruent to 7 mod 13 (215324) is congruent to - 7 mod 13 (215428) is congruent to -7 mod 13

2018-12-14, 12:24	#43
enzocreti Mar 2018 1022₈ Posts	coincidence If all these are coincidences, I am superman!

2018-12-14, 12:52	#44
enzocreti Mar 2018 2·5·53 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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