20021109, 10:27  #1 
2^{2}×431 Posts 
Mersenne composite using fibonacci
Let p= 1 mod 4
If Mp, does not divide F(Mp1), then Mp is composite. For example. 2^13466917 divides F(2^13466917 2) 
20021109, 10:30  #2 
3^{2}×367 Posts 
Oops,
2^13466917 1 divides F(2^13466917 2) And so may be prime! sure enough it is. 
20021109, 10:41  #3 
3^{2}·5·23 Posts 
What would take longer?
(a)The execution of the LucasLehmer test on 2^13466917 1 or, (b)Dividing F(2^13466917 2) by 2^13466917 1, make sure it is not compostie ? 
20021112, 18:07  #4  
Aug 2002
3×7 Posts 
Mersenne composite using fibonacci
Quote:


20021121, 10:54  #5 
2^{3}×3×229 Posts 
Well, Fibonacci numbers are smaller than the currently used Lehmer test numbers, but the algorithm lay undiscovered.
For example Lucas sequence 2,1, 3 ,4, 7 ,11,18,29... L(2^n) = 3, then 3^2 2 =7, then 7^22=47, and so on, just like Lehmer test but with a smaller starting number of three. I found more ! Let p be a prime>7 satisfying the following conditions: 1. p= 2,4(mod 5) 2. 2^[p+1] 3, is also prime Then (2^[p+1]3)  F(2^p1) Let p be a prime>5 satisfying the following conditions: 1. p = 4 (mod5) 2. 2^[p+1]1 is also prime Then(2^[p+1]1)  L(2^p1) 
20021123, 03:54  #6 
Aug 2002
2×3×5 Posts 
Never mind.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Listen and see how a composite, prime and mersenne responds to the drums  ONeil  ONeil  0  20180421 02:42 
2 holes in bizarre theorem about composite Mersenne Numbers  wildrabbitt  Math  120  20160929 21:52 
New Factor leaves a C168 Mersenne Composite  wblipp  ElevenSmooth  7  20130117 02:54 
Mersenne primes have highly composite p1?  ATH  Math  3  20090615 13:11 
Factoring highly composite Mersenne numbers  philmoore  Factoring  21  20041118 20:00 