20100802, 13:43  #1 
Aug 2010
SPb
2×17 Posts 
New test
Estimate please the test for simplicity of number
http://oeis.org/classic/A175625 a(i)=2*i+7; ((2*i+7) mod 3)> 0; (a(i) does not share on 3); 4^(i+3) == 1 (mod (2*i+7)); 4^(i+2) == 1 (mod (i+3)) The first compound number a(i)=536870911 It is found by the user "venco" (from http://dxdy.ru) It is interesting to notice that i+3=268435455=2^281 The second compound number a(i)=46912496118443 It is found by the user "venco" It is interesting to notice that i+3=268435455=(2^461)/3 Exceptions are defined if to prove that they share on numbers (2^x1) or (2^x+1) Excuse for my English 
20100803, 06:13  #2  
Aug 2010
SPb
100010_{2} Posts 
Quote:
i+3=23456248059221=(2^461)/3 Last fiddled with by wblipp on 20100803 at 19:52 

20100803, 17:34  #3 
Aug 2006
2^{2}·1,493 Posts 
I don't understand the sequence. Can you explain how you get 11, 23, 31, ...?

20100803, 19:31  #4 
Aug 2010
SPb
2·17 Posts 

20100803, 19:54  #5  
Aug 2006
2^{2}×1,493 Posts 
Quote:
"(2*i+7) mod 3)> 0", I guess, means that 2i + 7 is not divisible by 3. My guess is that your sequence is odd numbers a = 2i+7 such that


20100803, 20:03  #6  
Aug 2006
2^{2}·1,493 Posts 
Quote:


20100803, 20:15  #7 
Aug 2010
SPb
2×17 Posts 
to 10^15 There are only two exceptions
Both exceptions divisible by expression 2^x1 or 2^x+1 (If it was possible to prove it (What is the exception has such dividers).... It would be good) The first compound number a(i)=536870911 It is found by the user "venco" (from http://dxdy.ru) It is interesting to notice that i+3=268435455=2^281 The second compound number a(i)=46912496118443 It is found by the user "venco" It is interesting to notice that i+3=23456248059221=(2^461)/3 PS Such coincidence happens to mine only in the Indian cinema Last fiddled with by allasc on 20100803 at 20:23 
20100803, 20:25  #8 
Aug 2010
SPb
2×17 Posts 
Excuse for my English :)

20100803, 20:46  #9 
Aug 2006
5972_{10} Posts 

20100803, 21:22  #10 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,663 Posts 
Аскар, опишите порусски, и я или ктонибудь другой переведет, ok?
Есть много "ложных друзей переводчика", например "простое" число это вовсе не "simple", a "prime". (We will translate from Russian to English.) 
20100803, 21:30  #11 
Aug 2006
2^{2}·1,493 Posts 
Batalov, would you comment on the simple/prime and compound/composite issue? This came up on the seqfans list recently (with another native Russian speaker) and I was reminded of it here. I asked a Ukrainian colleague about it, but she doesn't know the math terms in Russian...
Last fiddled with by CRGreathouse on 20100803 at 21:30 
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