On May 3, 2024, Davide Rotondo sent the following
conjecture:
TEST FOR TWIN PRIMES AND PSEUDOTWIN PRIMES to BASE 3
FOR n>3,
A PAIR OF NUMBERS (n,n+2) PASS THE TEST IF
(3(3^(n-1)-1)+n*(floor((n-2)/3))) is a multiple of n*(n+2).
Examples:
1) 89 & 91:
(3(3^(89-1)-1)+89*(floor((89-2)/3)))/(89*91) =
359219803600761922290463739534787312839
2) 3 &5:
(3(3^(5-1)-1)+5*(floor((5-2)/3)))/(5*7) = 7
Q. true or false?
From Jun 8 to 14, 2024,
contributions came from Alessandro Casini
***
Alessandro wrote:
I'm sorry but I
can't grasp the content of the conjecture. The test is ok, but
what is hypothesized?
Not that all pairs
of numbers that pass the test are twin primes, because n = 89
itself would be a counterexample.
***
