20020918, 18:31  #1 
16765_{8} Posts 
Twin Primes
Hi. All this is pretty new to me and my maths is weak so forgive me if this is a daft question.
What are the chances that M39 (or one of the others) is the lower half of a twin prime? ie. M39 + 2 is also prime. Is it even possible? 
20020918, 22:08  #2 
Aug 2002
A Dyson Sphere
3^{2}×7 Posts 
I am not sure but i do not think that it is possible. I say this because we know that M39 is not divisible by 3 because it is prime. M39+1 is not divisible by 3 either because it is a power of 2. So M39+2 must be divisible by 3.

20020918, 22:22  #3 
Banned
"Luigi"
Aug 2002
Team Italia
2^{6}×3×5^{2} Posts 
Uhm... a Mersenne Prime should be a string of binary "1" . If you add 2 (that is "10") to a Mersenne Prime the result won't give you a string of ones. That is, you won't get a Mersenne Prime anymore.
Luigi (where did I go wrong? :( ) 
20020918, 22:26  #4  
Banned
"Luigi"
Aug 2002
Team Italia
12C0_{16} Posts 
Quote:
Next time I'll read the post and connect my brain before answering, sorry. Luigi 

20020918, 22:41  #5  
2^{4}·17·31 Posts 
Quote:
(Maybe I should have posted this in the maths forum. Sorry.) 

20020918, 22:45  #6 
Sep 2002
2^{2}×3×5 Posts 
powers of 2 are only divisible by 2 because 2 is its only prime factor. For example, 8 is 2x2x2. 16 is 2x2x2x2, etc.

20020918, 22:48  #7 
Sep 2002
111100_{2} Posts 
Also, I forgot to say that powers of any prime number are only divisible by that prime number, because it is its only prime factor. 81 = 3x3x3x3, 125 = 5x5x5, etc.

20020919, 19:01  #8 
Aug 2002
Portland, OR USA
112_{16} Posts 
Twin Primes
Maybe this has already been answered above and I got lost, but ...
What about the possibility of adjacent Mersennes (having Twin Primes as exponents) both being prime? examples: M(5), M(7) and M(17), M(19). So can there be more like that, or is there some relationship that prevents it? I guess a formal way to ask it would be: Can M(6k  1) and M(6k + 1) both be prime for k > 3? 
20020919, 19:06  #9 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}×919 Posts 
Mp could be the upper number in a twin prime. Will Edgington kept data on this at:
http://www.garlic.com/~wedgingt/M3status.txt It looks like no one has attacked M39  2 
20020920, 07:49  #10  
Aug 2002
Rovereto (Italy)
3·53 Posts 
Quote:
eng. version: Hi Luigi! Could you explain why it happens? Thanks and regards! Guido 

20020920, 09:18  #11  
Banned
"Luigi"
Aug 2002
Team Italia
1001011000000_{2} Posts 
Quote:
2^2 = 4 = 100b > 2^2  1 = 3 = 11b 2^3 = 8 = 1000b > 2^3  1 = 7 = 111b 2^5 = 32 = 100000b > 2^5  1 = 31 = 11111b 2^7 = 128 = 10000000 > 2^7  1 = 127 = 1111111b ... 2^n = 1(0)n b > 2^n  1 = (1)n b (1)n means a string of n "1" Luigi 

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