20180820, 19:17  #1 
Dec 2011
After milion nines:)
3·7·71 Posts 
Poisson Distribution
Tell me how calculate Poisson Distribution for sequence 95*10^n1
Know exponent (primes ) are 3,192,1133,4763,5812,48467,130620,466002 What will be next expected exponent that yield prime? 
20180820, 19:36  #2  
Sep 2003
5·11·47 Posts 
Quote:
But assuming it's a Poisson process, can you really predict anything useful about where to look for the next one? 

20180820, 22:55  #3  
Dec 2011
After milion nines:)
3×7×71 Posts 
Quote:
I am working on this sequence for years, so I do know where prime is not :) 

20180821, 19:24  #4 
Aug 2006
5979_{10} Posts 
OK. The primes 2, 5, and 19 divide 95*10, so none of these will be a factor. This increases the chance your numbers will be prime by a factor of
. You could do more work with the cycle lengths of other primes to refine the value of , but I'll ignore those for now. The 'chance' that 95*10^n1 is prime can now be approximated by Let's say you haven't tested past 466002. To get a symmetric 95% confidence interval you want a 2.5% chance on the left and a 2.5% chance on the right. How much Poisson mass do you need to make that happen? On the left, you want 0.025 = 1  e^x, so log(1  .025); on the right, log(1  .975). A little bit of calculus suggests that the answer is about and and so a prime 'should' appear between 467949 and 855160. But these look pretty small and close together compared to my intuition, which suggests to me that the effect of the cycle lengths of the small primes is important and shouldn't be ignored. Last fiddled with by CRGreathouse on 20180821 at 19:25 
20180821, 20:08  #5  
Dec 2011
After milion nines:)
2723_{8} Posts 
Quote:
I also hope that will place where "prime" should appear, but now, I passed 1M5 without new prime. Would this new data have impact on your calculation? And thanks for answer! Last fiddled with by pepi37 on 20180821 at 20:10 

20180822, 12:17  #6  
Aug 2006
3·1,993 Posts 
Quote:
But see the caveat above: I think more analysis is needed, the intervals should be wider and larger (start higher and end much higher) because of the effect of the other primes beside 2, 5, and 19. 

20180828, 02:10  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2·11·449 Posts 
Ye're too much a math bookworm... ye may need to step out from the library from time to time, hehe... The notation is used a lot in engineering field, especially in electronics (values of components, resistors, etc, is usually written 6k8, because writing 6.8k can cause confusion on large schematics with small print where the dot will not really be visible  even here on the forum, is not, if you get closer to an age..), and it was used in the past repeatedly and frequently on the forum too.
OTOH, we like your post with the calculus, and we learned something interesting from it... (like usual, your posts are quite interesting). Few weeks ago we struggled to teach our little LaurV who's studying abroad, about confidence intervals (she has a half semester statistics, big pain for a future biologist, haha), using skype/paint as scratchpad, and it was a pain in the but, because we also forgot some stuff we didn't use in years, and it was a lot of "cries" on both sides... hehe... fun time... Last fiddled with by LaurV on 20180828 at 02:16 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Distribution of primegaps  ATH  Prime Gap Searches  63  20191006 22:37 
Help with probability distribution.  Unregistered  Information & Answers  13  20110715 15:12 
exponential distribution  davieddy  Puzzles  10  20100525 03:43 
LLR Version 3.7.1c distribution  Jean Penné  Software  49  20080430 17:13 
Poisson processes prescription, please?  Fusion_power  Information & Answers  5  20070815 14:20 