20181214, 05:45  #34 
Mar 2018
17·31 Posts 
unusual
No this is not unusual i agree...
anyway the multiples of 215 and 36, that are unusual 
20181214, 06:36  #35 
Aug 2006
3·1,987 Posts 
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.

20181214, 07:23  #36  
Mar 2018
17×31 Posts 
I CANT
Quote:
NO I cant I am not Andrew Wiles!!! 

20181214, 07:37  #37 
Aug 2006
5961_{10} Posts 
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 20181214 at 07:38 
20181214, 09:37  #38 
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 20181214 at 09:39 
20181214, 10:23  #39 
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. 
20181214, 10:33  #40 
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 
20181214, 10:58  #41 
Mar 2018
17×31 Posts 
215*
Moreover:
215 is congruent to (2^31) mod 111 215*324 is congruent to (2^61) mod 111 215*428 is congruent to (2^11) mod 111 
20181214, 12:23  #42 
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 
20181214, 12:24  #43 
Mar 2018
1000001111_{2} Posts 
coincidence
If all these are coincidences, I am superman!

20181214, 12:52  #44 
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 20181214 at 12:55 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Unique Groupings found in the first 49 mersenne numbers  ONeil  ONeil  27  20181203 01:52 
I think I found proof that no odd perfect numbers exist!  Philly314  Aliquot Sequences  3  20141116 14:58 
Have Found Principle to generate infinitive PRIME NUMBERS  Evgeny Dolgov  Miscellaneous Math  38  20100905 17:45 
Can You See The Patterns..?  wustvn  Puzzles  7  20081120 14:00 
Shortest sequence of numbers not found in M43  Xyzzy  Miscellaneous Math  41  20081108 17:57 