Tuesday, June 29, 2004
Approaching a twin primes conjecture proof
The twin primes conjecture is that there are an infinity of twin primes which are primes separated by 2. For instance, 5 and 7 are twin primes, as 7-5 = 2.
Here's an idea that's a variant on the proof of the infinitude of primes, might not be new, but why not throw it out there?
Multiply every prime except 3 up to some arbitrary j-th prime. Now add 1.
The result is either divisible by 3 or has a residue of -1 or 1 with respect to 3.
If the result is not divisible by 3 it is prime.
If the result is has a resdiue of -1, then when you add 2 to it, the result is prime, so you have a paired prime.
Now then, all you have to do is prove that there will be a continuous cycling between possibilities of 0, -1 and 1 residues with respect to 3.
Example:
2(5) = 10 + 1 = 11 = -1 mod 3, and 13 is prime
Now then, someone out there who wants worldwide fame in math circles just needs to prove that you will always find a product P of a series of primes with 3 left out such that P = -1 mod 3.
Have fun!
Here's an idea that's a variant on the proof of the infinitude of primes, might not be new, but why not throw it out there?
Multiply every prime except 3 up to some arbitrary j-th prime. Now add 1.
The result is either divisible by 3 or has a residue of -1 or 1 with respect to 3.
If the result is not divisible by 3 it is prime.
If the result is has a resdiue of -1, then when you add 2 to it, the result is prime, so you have a paired prime.
Now then, all you have to do is prove that there will be a continuous cycling between possibilities of 0, -1 and 1 residues with respect to 3.
Example:
2(5) = 10 + 1 = 11 = -1 mod 3, and 13 is prime
Now then, someone out there who wants worldwide fame in math circles just needs to prove that you will always find a product P of a series of primes with 3 left out such that P = -1 mod 3.
Have fun!
# posted by James Harris @ 17:55 
