20061029, 22:32  #1 
"Jason Goatcher"
Mar 2005
5·701 Posts 
Weird occurrence
Over in Seventeen or Bust forum, someone tested 2*11^n+1 numbers for primality, and discovered the following:
2*11^11325+1 2*11^11325+1 Divides Phi(11^11325,2) 2*11^13359+1 2*11^13359+1 Divides Phi(11^13359,2) 2*11^11325+1 2*11^11325+1 Divides Phi(11^11325,2) 2*11^13359+1 2*11^13359+1 Divides Phi(11^13359,2) They were wondering if anyone can explain this? Please note: I have no idea what Phi means, I'm just trying to help out my friends, so if someone could give me something that I can simply copy and paste, I would be very grateful. 
20061031, 06:03  #2 
Feb 2005
2^{2}·3^{2}·7 Posts 
Can you give a link to the original topic in Seventeen or Bust forum? Thanks.

20061031, 21:24  #3 
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 
Here is the thread:
http://www.freedc.org/forum/showthread.php?t=3146 
20061105, 05:06  #4 
Feb 2005
2^{2}×3^{2}×7 Posts 
Please explain what is the function Phi(x,y).

20061112, 00:16  #5 
Jan 2005
Minsk, Belarus
2^{4}×5^{2} Posts 

20061112, 22:24  #6  
Feb 2005
11111100_{2} Posts 
Quote:
Note that 2 is a square modulo p (the Legendre symbol (2/p)=1), implying that the multiplicative order of 2 divides (p1)/2=11^k. The multiplicative order is smaller than (p1)/2 only if 2 is the 11th power modulo p. Being the 11th power is less likely than notbeing (roughly in 10 times). Perhaps, there exist examples when 2 is the 11th power modulo p but they are harder to find. Last fiddled with by maxal on 20061112 at 22:29 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Dr Nicely's 1st occurrence Prime Gaps  rudy235  Prime Gap Searches  192  20200206 09:48 
Weird  Dubslow  YAFU  14  20160106 19:34 
This is weird... Isn't it?  guido72  PrimeNet  18  20150611 16:18 
A 1 in 1,852 occurrence!  NBtarheel_33  Data  27  20090325 03:33 
something very weird  ixfd64  PrimeNet  1  20081016 18:19 