20220804, 01:52  #45  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:


20220804, 01:52  #46  
Apr 2020
857 Posts 
Quote:


20220804, 02:04  #47  
Apr 2020
857_{10} Posts 
Then why did you ask whether it was finite or infinite?
Quote:
1. There is some asyetundiscovered property of p(n) for n odd that makes it much, much less likely to be part of a cousin prime pair than a random number of the same size would be. 2. Those 5 consecutive even terms are a coincidence. 

20220804, 02:49  #48  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:
There is no single known odd composite term, and there is no single known term > 3 which is == 3 mod 4 Last fiddled with by sweety439 on 20220804 at 02:49 

20220804, 11:50  #49  
Feb 2017
Nowhere
2×2,999 Posts 
Quote:
But  the index suddenly jumps from 2732 to 19439060  surely there must be something going on! Argle bargle! Argle bargle! 

20220804, 12:08  #50  
Apr 2020
857 Posts 
Quote:
I'm sure that if we were in the 1950s and this was the full known extent of the sequence, you'd have been speculating that there are no more odd terms. When the next term was discovered to be 417, you'd have said that maybe there are no terms that are 3 mod 4 apart from 3. And then it turns out 491 is in the sequence. It's easy to go looking for patterns. But if it's not outrageously unlikely for them to have appeared by chance, and there's no good reason for them to exist, you shouldn't expect them to continue forever. 

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