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Forum: sweety439 2022-02-05, 14:21
Replies: 3
Views: 1,503
Posted By sweety439
Notable factorization of Phi(n,2)

n (Phi(n,2) is (2*n+1) * prime) Phi(2*n,2) Phi(4*n L,2) & Phi(4*n M,2) Phi(8*n,2)
11 (23 * prime) prime both prime composite (divisible by 353)
23 (47 * prime) prime both...
Forum: sweety439 2020-10-25, 09:39
Replies: 3
Views: 1,503
Posted By sweety439
* If p is larger, then Rp(b) is harder to be...

* If p is larger, then Rp(b) is harder to be prime, the smallest base b such that Rp(b) is prime is about gamma*p (gamma is the Euler constant 0.577215664901...)

In general .... (let Rp(b) =...
Forum: sweety439 2020-10-17, 09:38
Replies: 3
Views: 1,503
Posted By sweety439
M5 = 31, M7 = 127, W5 = 11, W7 = 43 It is...

M5 = 31, M7 = 127, W5 = 11, W7 = 43

It is known that MM5, MM7, WW5, WW7 are primes

However, MMM5 and WWW5 are both known to be composite

Two open problems: Is MMM7 prime? Is WWW7 prime?

I...
Forum: sweety439 2020-10-17, 06:55
Replies: 3
Views: 1,503
Posted By sweety439
Some notable smallest repunit/nexus prime

Let

a(b) = Smallest prime p such that the generalized repunit number (b^p-1)/(b-1) is prime
b(p) = Smallest base b such that the generalized repunit number (b^p-1)/(b-1) is prime
c(b) = Smallest...
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