mersenneforum.org - View Single Post - Largest k*2^n-1 Primes Found In 2017

George M · 2018-01-02, 05:37

Doing a little bit of research, these primes are called “Proth Primes”. We also have the Prime Gap Equation which when writing in TEX, I accidentally forgot to add 2 to the RHS. Here is the clean version.

$p_{n+1} \ = \ \{2 \ + \ \sum_{k = 1}^n(p_{k + 1} \ - \ p_k) \ : \ p_m \ = \ m^{th} \ prime \ number\}$

I mentioned this equation on three or four other threads I believe (Conjectures R Us, Prime Gap News, Predict M50/M51, etc) for I was trying to find a proof. Does anyone have a proof of this equation?

2018-01-02, 05:37	#8
George M Dec 2017 50₁₀ Posts	I believe these primes are called “Proth Primes” Doing a little bit of research, these primes are called “Proth Primes”. We also have the Prime Gap Equation which when writing in TEX, I accidentally forgot to add 2 to the RHS. Here is the clean version. $p_{n+1} \ = \ \{2 \ + \ \sum_{k = 1}^n(p_{k + 1} \ - \ p_k) \ : \ p_m \ = \ m^{th} \ prime \ number\}$ I mentioned this equation on three or four other threads I believe (Conjectures R Us, Prime Gap News, Predict M50/M51, etc) for I was trying to find a proof. Does anyone have a proof of this equation? Last fiddled with by George M on 2018-01-02 at 05:38