Problems & Puzzles: Conjectures
Conjecture 83. Two conjectures about primes
Dmitry Kamenetsky wrote on March 10, 2019
I have two conjectures:
C1) For any prime p>3 there exists a prime q<p, such that 2p+q is prime.
C2) For any prime p>3 there exists a prime q<p, such that 4p+q is prime.
I have checked that they work for p<10000, but I don't know if they always work.
Q. Can anyone prove C1/C2 or find a counter example?
On Dec 6, 2019, Dmitry wrote:I think these conjectures are somehow related to the Goldbach conjecture and are thus difficult to prove. I have created sequences for them, which you may want to add:
Records | Conjectures | Problems | Puzzles