Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Definition :

Let $W_p$ be a Wagstaff number of the form :

$W_p=\frac{2^p+1}{3}$ , with $p\equiv 1 \pmod 4$

Next , define sequence $S_i$ as :

$S_i = \begin{cases} 3/2, & i=0 \\ 8S^4_{i-1}-8S^2_{i-1}+1, & i>0 \end{cases}$

How to prove following statement :

Conjecture :

$W_p$ is a prime iff $S_{\frac{p-1}{2}} \equiv \frac{3}{2} \pmod {W_p}$

I checked statement for following Wagstaff primes :

$W_5 , W_{13} , W_{17} , W_{61} , W_{101} , W_{313} , W_{701} , W_{1709} , W_{2617} , W_{10501} , W_{42737} ,W_{95369} , W_{138937} ,W_{267017}$

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.