Thursday, September 20, 2007
Primes conjecture with surrogate factoring
Oddly enough looking at going in a different direction with what I call the surrogate factoring congruence lead me to a fascinating little result!
Given a composite S, it is not possible for abs(S - 2k^2) to be prime for any non-zero k, unless S is a product of two primes, and they have to be differing primes.
Is that already known?
It is kind of an odd little result. Here's an example of when a prime is allowed, S = 77, k = 6, then
77 - 2*36 = 5
but in contrast, say if S = 105, which has 3 prime factors, by this conjecture no non-zero k exists such that
abs(105 - 2k^2)
is a prime number.
The proof is oddly easy but I'll call it a conjecture in case I made a mistake in the argument which can be found at my math blog.
Given a composite S, it is not possible for abs(S - 2k^2) to be prime for any non-zero k, unless S is a product of two primes, and they have to be differing primes.
Is that already known?
It is kind of an odd little result. Here's an example of when a prime is allowed, S = 77, k = 6, then
77 - 2*36 = 5
but in contrast, say if S = 105, which has 3 prime factors, by this conjecture no non-zero k exists such that
abs(105 - 2k^2)
is a prime number.
The proof is oddly easy but I'll call it a conjecture in case I made a mistake in the argument which can be found at my math blog.
# posted by James Harris @ 20:49 
